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Jun 29, 2018
06/18

by
Zuzana Buckova; Beata Stehlikova; Daniel Sevcovic

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In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend also on other stochastic factors. Our focus is on convergence models, which explain the evolution of interest rate in connection with the adoption of Euro currency. Here, the domestic short rate depends on a...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1607.04968

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3.0

Jun 30, 2018
06/18

by
Giovanni Mottola

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We study the solution's existence for a generalized Dynkin game of switching type which is shown to be the natural representation for general defaultable OTC contract with contingent CSA. This is a theoretical counterparty risk mitigation mechanism that allows the counterparty of a general OTC contract to switch from zero to full/perfect collateralization and switch back whenever she wants until contract maturity paying some switching costs and taking into account the running costs that emerge...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1410.0594

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4.0

Jun 30, 2018
06/18

by
Jihun Han; Hyungbin Park

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The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk. The purpose of this article is to determine upper and lower bounds on the risk premium of an asset based on the market prices of options. One of the key assumptions to achieve this goal is that the market is Markovian. Under this...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1411.4606

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22

Jun 26, 2018
06/18

by
Philipp Harms; David Stefanovits; Josef Teichmann; Mario Wüthrich

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The analytical tractability of affine (short rate) models, such as the Vasicek and the Cox-Ingersoll-Ross models, has made them a popular choice for modelling the dynamics of interest rates. However, in order to account properly for the dynamics of real data, these models need to exhibit time-dependent or even stochastic parameters. This in turn breaks their tractability, and modelling and simulating becomes an arduous task. We introduce a new class of Heath-Jarrow-Morton (HJM) models that both...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1502.02926

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4.0

Jun 30, 2018
06/18

by
A. Kushpel; J. Levesley

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Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an analytic extension into an appropriate tube and "bell-shaped" with rapidly decaying tails. Unfortunately, the domain of such functions is not compact which creates various technical difficulties. We solve interpolation problem on an infinite rectangular...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1404.5271

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4.0

Jun 30, 2018
06/18

by
René Aid; Salvatore Federico; Huyên Pham; Bertrand Villeneuve

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We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpreta- tions for three models of demand (arithmetic Brownian, geometric Brownian, and the Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the in- vestment in the pipeline, must never drop below the best predictor of future...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.0055

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8.0

Jun 29, 2018
06/18

by
Francesca Biagini; Jacopo Mancin; Thilo Meyer Brandis

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In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a contin- uous financial market with two assets, where the discounted risky one is modeled as a symmetric G-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.05484

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4.0

Jun 28, 2018
06/18

by
Vladimir Vovk

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This paper gives several simple constructions of the pathwise Ito integral $\int_0^t\phi d\omega$ for an integrand $\phi$ and a price path $\omega$ as integrator, with $\phi$ and $\omega$ satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither $\phi$ nor $\omega$ are assumed to be paths of stochastic processes, and the Ito integral exists almost surely in a non-probabilistic financial sense. For example, one of the results shows the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.01698

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3.0

Jun 28, 2018
06/18

by
Frank Gehmlich; Thorsten Schmidt

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The intensity of a default time is obtained by assuming that the default indicator process has an absolutely continuous compensator. Here we drop the assumption of absolute continuity with respect to the Lebesgue measure and only assume that the compensator is absolutely continuous with respect to a general $\sigma$-finite measure. This allows for example to incorporate the Merton-model in the generalized intensity based framework. An extension of the Black-Cox model is also considered. We...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.03896

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8.0

Jun 30, 2018
06/18

by
Jean-Pierre Fouque; Ruimeng Hu

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Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index $H \in (0,1)$). We rigorously establish a first order approximation of the optimal value, where the return and...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.06969

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7.0

Jun 29, 2018
06/18

by
Guglielmo D'Amico

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The article presents a general discrete time dividend valuation model when the dividend growth rate is a general continuous variable. The main assumption is that the dividend growth rate follows a discrete time semi-Markov chain with measurable space. The paper furnishes sufficient conditions that assure finiteness of fundamental prices and risks and new equations that describe the first and second order price-dividend ratios. Approximation methods to solve equations are provided and some new...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1605.02472

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10.0

Jun 29, 2018
06/18

by
Yiran Cui; Sebastian del Bano Rollin; Guido Germano

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Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-call parity. Solving for the implied volatility that reproduces a given market price yields not only a real root, but also infinitely many complex roots in a neighbourhood of the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1612.01951

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8.0

Jun 29, 2018
06/18

by
Weston Barger; Matthew Lorig

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We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process. Rigorous accuracy results are provided for European-style claims. For barrier-style claims, we include several numerical examples to illustrate the accuracy and versatility of...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.05728

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4.0

Jun 29, 2018
06/18

by
Peter Bank; Yan Dolinsky

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We study super-replication of contingent claims in markets with fixed transaction costs. The first result in this paper reveals that in reasonable continuous time financial market the super--replication price is prohibitively costly and leads to trivial buy--and--hold strategies. Our second result is derives non trivial scaling limits of super--replication prices in the binomial models with small fixed costs.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.09234

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7.0

Jun 29, 2018
06/18

by
Tanmay S. Patankar

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This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models have been well-documented. This project extends that notion to a class of semi-Markov processes known as age-dependent processes. We also allow for time-dependence in volatility within regimes. We show that the problem of option pricing in such...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1609.04907

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4.0

Jun 29, 2018
06/18

by
Stefan Gerhold; I. Cetin Gülüm

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Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a bid-ask spread. The main question then is how large (in terms of a deterministic bound) this spread must be to explain the given prices. We fully solve this problem in the case of a single maturity, and give several partial results for multiple maturities....

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.05585

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7.0

Jun 30, 2018
06/18

by
Saul Jacka; Seb Armstrong; Abdelkarem Berkaoui

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We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\mathcal{F}_t$: the $t^{th}$ cone in the sum contains bounded random variables that are $\mathcal{F}_t$-measurable. Hence we obtain a generalisation of Delbaen's m-stability condition for the problem of reserving in a collection of num\'eraires $\mathbf{V}$, called $\mathbf{V}$-m-stability, provided these cones arise from acceptance sets of a dynamic coherent...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.03638

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5.0

Jun 29, 2018
06/18

by
Miles B. Gietzmann; Adam J. Ostaszewski

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Following the approach of standard filtering theory, we analyse investor-valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold their observations; explicit filtering formulas are derived for downgrading the valuations in the absence of disclosures. The analysis is conducted for both a solitary firm and m...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1606.04039

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21

Jun 27, 2018
06/18

by
Alexander von Felbert

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In this paper we offer a novel type of network model which can capture the precise structure of a financial market based, for example, on empirical findings. With the attached stochastic framework it is further possible to study how an arbitrary network structure and its expected counterparty credit risk are analytically related to each other. This allows us, for the first time, to model the precise structure of an arbitrary financial market and to derive the corresponding expected exposure in...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1504.06789

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32

Jun 26, 2018
06/18

by
Sabrina Mulinacci

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A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copulas and the Scale Mixture of Marshall-Olkin copulas (see Li, 2009),are obtained through suitable distortions of bivariate Archimedean copulas: this induces asymmetry, and the...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1502.01912

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16

Jun 27, 2018
06/18

by
Alain Bélanger; Gaston Giroux; Ndouné Ndouné

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The extended Wild sums considered in this article generalize the classi- cal Wild sums of statistical physics. We first show how to obtain explicit solutions for the evolution equation of a large system where the interactions are given by a single, but general, interacting kernel which involves m components, for a fixed m >= 2. We then show how to retain the explicit formulas for the case of OTC market models where the dynamics is more directly described by two (or more) kernels.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1503.03006

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3.0

Jun 30, 2018
06/18

by
Xiaoxiao Zheng; Xin Zhang

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In this paper, we consider the optimal dividend problem for a company. We describe the surplus process of the company by a diffusion model with regime switching. The aim of the company is to choose a dividend policy to maximize the expected total discounted payments until ruin. In this article, we consider a hybrid dividend strategy, that is, the company is allowed to conduct continuous dividend strategy as well as impulsive dividend strategy. In addition, we consider the change of economy,...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.7606

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6.0

Jun 30, 2018
06/18

by
Andrei Lebedev; Petr Zabreiko

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In the article a strenthened version of the 'Fundamental Theorem of asset Pricing' for one-period market model is proven. The principal role in this result play total and nonanihilating cones.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1412.7058

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10.0

Jun 27, 2018
06/18

by
Huiwen Yan; Zhou Yang; Fahuai Yi; Gechun Liang

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This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian setting, we investigate the optimal strategy by analyzing the properties of the corresponding free boundary, including its position, asymptotics, monotonicity and regularity. We...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1503.08961

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4.0

Jun 30, 2018
06/18

by
Johan GB Beumee; Chris Cormack; Peyman Khorsand; Manish Patel

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This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which also preserves the proper state equation of motion. Many numerical numerical examples of this process are provided. For a smaller grid the probability construction converges into a...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.0077

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18

Jun 27, 2018
06/18

by
Si Cheng; Michael R. Tehranchi

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In this article, we explore a class of tractable interest rate models that have the property that the price of a zero-coupon bond can be expressed as a polynomial of a state diffusion process. Our results include a classification of all such time-homogeneous single-factor models in the spirit of Filipovic's maximal degree theorem for exponential polynomial models, as well as an explicit characterisation of the set of feasible parameters in the case when the factor process is bounded. Extensions...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1504.03238

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6.0

Jun 30, 2018
06/18

by
Sabrina Mulinacci

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In this paper we study the distributional properties of a vector of lifetimes in which each lifetime is modeled as the first arrival time between an idiosyncratic shock and a common systemic shock. Despite unlike the classical multidimensional Marshall-Olkin model here only a unique common shock affecting all the lifetimes is assumed, some dependence is allowed between each idiosyncratic shock arrival time and the systemic shock arrival time. The dependence structure of the resulting...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1704.02160

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19

Jun 27, 2018
06/18

by
Tim Leung; Kazutoshi Yamazaki; Hongzhong Zhang

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We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence the solutions in general cannot be attained analytically. Motivated by the maturity randomization (Canadization) technique by Carr (1998), we approximate the refraction times by...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1505.07705

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Jun 28, 2018
06/18

by
Erik Ekström; Juozas Vaicenavicius

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We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1509.00686

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4.0

Jun 29, 2018
06/18

by
David Hobson; Anthony Neuberger

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The purpose of this note is to reconcile two different results concerning the model-free upper bound on the price of an American option, given a set of European option prices. Neuberger (2007, `Bounds on the American option') and Hobson and Neuberger (2016, `On the value of being American') argue that the cost of the cheapest super-replicating strategy is equal to the highest model-based price, where we search over all models which price correctly the given European options. Bayraktar, Huang...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1604.02274

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6.0

Jun 29, 2018
06/18

by
Nuno Azevedo; Diogo Pinheiro; Stylianos Xanthopoulos; Athanasios Yannacopoulos

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Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa-Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor's priors there exists a probability measure under which all admissible wealth processes are supermartingales. Furthermore, we show that under a certain attainability condition (which is always valid in finite or complete markets) this is also equivalent to the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.02446

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5.0

Jun 29, 2018
06/18

by
Zdzislaw Brzezniak; Tayfun Kok

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In this paper we study the stochastic evolution equation (1.1) in martingale-type 2 Banach spaces (with the linear part of the drift being only a generator of a C0-semigroup). We prove the existence and the uniqueness of solutions to this equation. We apply the abstract results to the Heath-Jarrow-Morton-Musiela (HJMM) equation (6.3). In particular, we prove the existence and the uniqueness of solutions to the latter equation in the weighted Lebesgue and Sobolev spaces respectively. We also...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.05814

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6.0

Jun 29, 2018
06/18

by
Yuki Shigeta

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In this paper, we study optimal switching problems under ambiguity. To characterize the optimal switching under ambiguity in the finite horizon, we use multidimensional reflected backward stochastic differential equations (multidimensional RBSDEs) and show that a value function of the optimal switching under ambiguity coincides with a solutions to multidimensional RBSDEs with allowing negative switching costs. Furthermore, we naturally extend the finite horizon problem to the infinite horizon...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.06045

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5.0

Jun 28, 2018
06/18

by
Gechun Liang; Thaleia Zariphopoulou

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In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward processes and infinite horizon BSDE, and, moreover, with risk-sensitive optimization. In addition, we develop a connection, for large time horizons, with a family of classical...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1511.04863

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6.0

Jun 30, 2018
06/18

by
Tim Leung; Xin Li; Zheng Wang

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This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit the same optimal starting and/or stopping strategies. We rigorously prove that the optimal starting and stopping strategies are of threshold type, and give the analytical...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1411.6080

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7.0

Jun 30, 2018
06/18

by
Alessandra Cretarola; Gianna Figà Talamanca

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We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices causing a Bubble effect, the presence of which is documented in several papers about the cryptocurrency. In this paper we develop a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as the behavior of a second factor...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.00215

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5.0

Jun 29, 2018
06/18

by
Kristoffer Lindensjö

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The optimal investment problem is one of the most important problems in mathematical finance. The main contribution of the present paper is an explicit formula for the optimal portfolio process. Our optimal investment problem is that of maximizing the expected value of a standard general utility function of terminal wealth in a standard complete Wiener driven financial market. In order to derive the formula for the optimal portfolio we use the recently developed functional It\^o calculus and...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.05018

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7.0

Jun 29, 2018
06/18

by
Candia Riga

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This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a pathwise self-financial condition for continuous-time trading strategies, which is consistent with the classical definition in case a probability model is introduced. Our first...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.04946

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3.0

Jun 30, 2018
06/18

by
Junbeom Lee; Chao Zhou

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In this paper, we investigate conditions to represent derivative price under XVA explicitly. As long as we consider different borrowing/lending rates, XVA problem becomes a non-linear equa- tion and this makes finding explicit solution of XVA difficult. It is shown that the associated valuation problem is actually linear under some proper conditions so that we can have the same complexity in pricing as classical pricing theory. Moreover, the conditions mentioned above is mild in the sense that...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.00259

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6.0

Jun 30, 2018
06/18

by
Kim Weston

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We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity. After establishing the existence of a discrete-time equilibrium, we show that the discrete-time equilibrium converges to a continuous-time equilibrium model. The continuous-time equilibrium provides an explicit formula for the equilibrium interest rate in terms of...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.01706

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Jun 30, 2018
06/18

by
Kasper Larsen; Halil Mete Soner; Gordan Žitković

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We introduce the notion of a conditional Davis price and study its properties. Our ultimate goal is to use utility theory to price non-replicable contingent claims in the case when the investor's portfolio already contains a non-replicable component. We show that even in the simplest of settings - such as Samuelson's model - conditional Davis prices are typically not unique and form a non-trivial subinterval of the set of all no-arbitrage prices. Our main result characterizes this set and...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.02087

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Jun 27, 2018
06/18

by
Ramin Okhrati; Alejandro Balbás; José Garrido

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In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on no prior default. More precisely, in this particular framework, the locally risk-minimizing approach is carried out when the underlying process has jumps, the derivative is...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1505.03501

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7.0

Jun 29, 2018
06/18

by
Gunther Leobacher; Michaela Szölgyenyi; Stefan Thonhauser

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We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.04660

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6.0

Jun 29, 2018
06/18

by
Francesca Biagini; Yinglin Zhang

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In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model guarantees not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by explicit...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.07910

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Jun 27, 2018
06/18

by
Archil Gulisashvili; Frederi Viens; Xin Zhang

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We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small-time behaviors of the above depend heavily on the model, and require a control of the asset price density which is uniform with respect to the asset price variable, in order to...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1505.05256

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11

Jun 27, 2018
06/18

by
Takuji Arai

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We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk measure a good deal valuation; and study its properties. We also discuss superhedging cost and Fundamental Theorem of Asset Pricing for convex constrained markets.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1506.00396

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Jun 28, 2018
06/18

by
Dmitry Kramkov; Kim Weston

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In the problem of optimal investment with utility function defined on $(0,\infty)$, we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt $(A_p)$ condition for the power $p=1/(1-a)$, where $a\in (0,1)$ is a lower bound on the relative risk-aversion of the utility function. We construct a counterexample showing that this...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1507.05865

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5.0

Jun 29, 2018
06/18

by
Aleš Černý

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We examine optimal quadratic hedging of barrier options in a discretely sampled exponential L\'{e}vy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of hedging errors on prices is several times higher than the impact of other pricing biases studied in the literature.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1603.03747

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12

Jun 30, 2018
06/18

by
Tim Leung; Hongzhong Zhang

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Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing buy and then sell an asset subject to a trailing stop. Under a general linear diffusion framework, we study an optimal double stopping problem with a random path-dependent maturity. Specifically, we first derive the optimal liquidation strategy prior to a given trailing stop, and prove the...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1701.03960

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Jun 27, 2018
06/18

by
Michael V. Klibanov; Andrey V. Kuzhuget

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A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. This idea is verified on real market data for...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1503.03567