Non-homogeneous stochastic LQ control with regime switching and random coefficients

Lq-stochastic Control

Markov Regime Switching Stochastic Volatility

This is a project on modeling time-varying volatility of S&P 500 weely return for the years 1990 to 2012 using Bayesian methods. First, MCMC on the log-stochastic volatility (SV) model is implemented with simulation results analyzed. Second, I generalize the SV model to encompass regime-switching properties with the markov switching log-stochastic volatility (MSSV) model, under which, high-vola...

Numerical Solutions of Stochastic Control Problems for Regime-switching Systems

In this paper, we develop approximation methods for solving stochastic control problems. The systems under consideration involve regime switching, modulated by a continuous-time Markov chain. Using Markov chain approximation techniques, we construct discrete-time Markov chains having two components. In addition to convergence of the procedure, numerical experiments and remarks on controlled var...

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of th...

Stochastic Functional Differential Equation under Regime Switching

We discuss stochastic functional differential equation under regime switching dx t f xt, r t , t dt q r t x t dW1 t σ r t |x t |βx t dW2 t . We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially ...