Richard S. Ellis

Shlomo Ta&#x2019;asan

Large Deviation Analysis of a Droplet Model Having a Poisson Equilibrium Distribution

We establish existence of a continuous selection of multifunctions associated with quantum stochastic evolution inclusions under a general Lipschitz condition. The coefficients here are multifunctions but not necessarily Lipschitz.

Sheila Bishop

On Continuous Selection Sets of Non-Lipschitzian Quantum Stochastic Evolution Inclusions

We examine foreign exchange options in the jump-diffusion version of the Heston stochastic volatility
model for the exchange rate with log-normal jump amplitudes and the volatility model with log-uniformly distributed jump amplitudes. We assume that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semianalytical formula for the price of the foreign exchange European call option.

Rehez Ahlip

Ante Prodan

Pricing FX Options in the Heston/CIR Jump-Diffusion Model with Log-Normal and Log-Uniform Jump Amplitudes

We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model, extending a previous decomposition formula for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used for this purpose are nonanticipative. In particular, we also see that equivalent results can be obtained by using Functional It&#xf4; Calculus. Using the same generalizing ideas, we also extend to nonexponential models the alternative call option price decomposition formula written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both the anticipative and the nonanticipative cases.

Ra&#xfa;l Merino

Josep Vives

A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models

We propose a stochastic nonlinear system to model the gating activity coupled with the membrane potential for a typical neuron. It distinguishes two different levels: a macroscopic one, for the membrane potential, and a mesoscopic one, for the gating process through the movement of its voltage sensors. Such a nonlinear system can be handled to form a Hodgkin-Huxley-like model, which links those two levels unlike the original deterministic Hodgkin-Huxley model which is positioned at a macroscopic scale only. Also, we show that an interacting particle system can be used to approximate our model, which is an approximation technique similar to the jump Markov processes, used to approximate the original Hodgkin-Huxley model.

Mauricio Tejo

Stochastic Nonlinear Equations Describing the Mesoscopic Voltage-Gated Ion Channels

This paper considers an infinite-buffer queuing system with birth-death modulated Markovian arrival process (BDMMAP) with arbitrary service time distribution. BDMMAP is an excellent representation of the arrival process, where the fractal behavior such as burstiness, correlation, and self-similarity is observed, for example, in ethernet LAN traffic systems. This model was first apprised by Nishimura (2003), and to analyze it, he proposed a twofold spectral theory approach. It seems from the investigations that Nishimura&#x2019;s approach is tedious and difficult to employ for practical purposes. The objective of this paper is to analyze the same model with an alternative methodology proposed by Chaudhry et al. (2013) (to be referred to as CGG method). The CGG method appears to be rather simple, mathematically tractable, and easy to implement as compared to Nishimura&#x2019;s approach. The Achilles tendon of the CGG method is the roots of the characteristic equation associated with the probability generating function (pgf) of the queue length distribution, which absolves any eigenvalue algebra and iterative analysis. Both the methods are presented in stepwise manner for easy accessibility, followed by some illustrative examples in accordance with the context.

Arunava Maity

U. C. Gupta

A Comparative Numerical Study of the Spectral Theory Approach of Nishimura and the Roots Method Based on the Analysis of BDMMAP/G/1 Queue

The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control) with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.

Ewelina Seroka

Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems

We propose a feasible and constructive methodology which allows us to compute <i>pure hedging strategies</i> with respect to arbitrary square-integrable claims in incomplete markets. In contrast to previous works based on PDE and BSDE methods, the main merit of our approach is the flexibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff. In particular, the methodology can be applied to multidimensional quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. In order to demonstrate that our methodology is indeed applicable, we provide a Monte Carlo study on generalized F&#xf6;llmer-Schweizer decompositions, locally risk minimizing, and mean variance hedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.

Daniel Bonetti

Dorival Le&#xe3;o

Alberto Ohashi

Vin&#xed;cius Siqueira

A General Multidimensional Monte Carlo Approach for Dynamic Hedging under Stochastic Volatility

An optimal asset allocation problem for a quite general class of utility functions is discussed in a simple two-state Markovian regime-switching model, where the appreciation rate of a risky share changes over time according to the state of a hidden economy. As usual, standard filtering theory is used to transform a financial model with hidden information into one with complete information, where a martingale approach is applied to discuss the optimal asset allocation problem. Using a martingale representation coupled with stochastic flows of diffeomorphisms for the filtering equation, the integrand in the martingale representation is identified which gives rise to an optimal portfolio strategy under some differentiability conditions.

Tak Kuen Siu

A Stochastic Flows Approach for Asset Allocation with Hidden Economic Environment

Recently, Kurtz (2007, 2014) obtained a general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations covering also the case of stochastic differential equations with jumps. Following the original method of Yamada and Watanabe (1971), we give alternative proofs for the following two statements: pathwise uniqueness implies uniqueness in the sense of probability law, and weak existence together with pathwise uniqueness implies strong existence for stochastic differential equations with jumps.

M&#xe1;ty&#xe1;s Barczy

Zenghu Li

Gyula Pap

Yamada-Watanabe Results for Stochastic Differential Equations with Jumps

About this journal

Journal profile

Meet the editorial board

Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Special Issues

International Journal of Stochastic Analysis - Table of contents 2015

International Journal of Stochastic Analysis | Hindawi

title

International Journal of Stochastic Analysis

https://images.hindawi.com/journals/ijsa/ijsa.banner.jpg

International Journal of Stochastic Analysis