Related papers: The escape problem under stochastic volatility: th…
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and…
The Heston model is a popular stock price model with stochastic volatility that has found numerous applications in practice. In the present paper, we study the Riemannian distance function associated with the Heston model and obtain…
The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global…
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous…
We apply the escape-rate formalism to compute the shear viscosity in terms of the chaotic properties of the underlying microscopic dynamics. A first passage problem is set up for the escape of the Helfand moment associated with viscosity…
The main subject of the paper is an escape from a multi-well metastable potential on a time-scale of a formation of the quasi-equilibrium between the wells. The main attention is devoted to such ranges of friction in which an external…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We consider a model of surface-mediated diffusion with alternating phases of pure bulk and surface diffusion. For this process, we compute the mean exit time from a disk through a hole on the circle. We develop a spectral approach to this…
A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is…
The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientific fields. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to…
In this paper, we study boundary-value problems describing the exit distribution of finite-velocity random motions from prescribed domains. For the standard telegraph process, with and without drift, we derive the Dirichlet problems…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
In genetic circuits, when the mRNA lifetime is short compared to the cell cycle, proteins are produced in geometrically-distributed bursts, which greatly affects the cellular switching dynamics between different metastable phenotypic…
We consider the problem of determining escape probabilities from an interval of a general compound renewal process with drift. This problem is reduced to the solution of a certain integral equation. In an actuarial situation where only…
We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. The volatility process…
There is considerable current interest in the emergence of statistical correlations within a population of otherwise non-interacting Brownian particles subject to a common fluctuating environment or drive. Examples include global stochastic…