927 research outputs found
Approximation methods for hybrid diffusion systems with state-dependent switching processes : numerical algorithms and existence and uniqueness of solutions
By focusing on hybrid diffusions in which continuous dynamics and discrete events coexist, this work is concerned with approximation of solutions for hybrid stochastic differential equations with a state-dependent switching process. Iterative algorithms are developed. The continuous-state dependent switching process presents added difficulties in analyzing the numerical procedures. Weak convergence of the algorithms is established by a martingale problem formulation first. This weak convergence result is then used as a bridge to obtain strong convergence. In this process, the existence and uniqueness of the solution of the switching diffusions with continuous-state-dependent switching are obtained. Different from the existing results of solutions of stochastic differential equations in which the Picard iterations are utilized, Euler's numerical schemes are considered here. Moreover, decreasing stepsize algorithms together with their weak convergence are given. Numerical experiments are also provided for demonstration
Optimal control of risk process in a regime-switching environment
This paper is concerned with cost optimization of an insurance company. The
surplus of the insurance company is modeled by a controlled regime switching
diffusion, where the regime switching mechanism provides the fluctuations of
the random environment. The goal is to find an optimal control that minimizes
the total cost up to a stochastic exit time. A weaker sufficient condition than
that of (Fleming and Soner 2006, Section V.2) for the continuity of the value
function is obtained. Further, the value function is shown to be a viscosity
solution of a Hamilton-Jacobian-Bellman equation.Comment: Keywords: Regime switching diffusion, continuity of the value
function, exit time control, viscosity solutio
Fourier Transform Methods for Regime-Switching Jump-Diffusions and the Pricing of Forward Starting Options
In this paper we consider a jump-diffusion dynamic whose parameters are
driven by a continuous time and stationary Markov Chain on a finite state space
as a model for the underlying of European contingent claims. For this class of
processes we firstly outline the Fourier transform method both in log-price and
log-strike to efficiently calculate the value of various types of options and
as a concrete example of application, we present some numerical results within
a two-state regime switching version of the Merton jump-diffusion model. Then
we develop a closed-form solution to the problem of pricing a Forward Starting
Option and use this result to approximate the value of such a derivative in a
general stochastic volatility framework.Comment: 25 pages, 6 figure
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