Different regimes, for example, different seasons, bull market/bear market, multiple missions
etc., affect the performance of systems or products greatly in the real world. Thus, a dynamic …

We consider a class of one-dimensional (1D) reflected stochastic differential equations
(SDEs). Such reflected SDE models arise as the key approximating processes in a regulated …

In this paper, we investigate the price for the zero-coupon defaultable bond under a
structural form credit risk with regime switching. We model the value of a firm and the default …

Self-exciting point processes are applied to various fields such as seismology, finance,
neurophysiology, criminology, biology etc to model the clustering/contagion phenomenon …

We study a pricing barrier control problem in a regime-switching regulated market. In doing
so, we analyze a class of one-dimensional reflected regime-switching diffusion processes …

The contagion credit risk model is used to describe the contagion effect among different
financial institutions. Under such a model, the default intensities are driven not only by the …

A class of analytically tractable bivariate Markov modulated point process is presented in
this article. The intensities of the bivariate jump process are assumed to be driven by a …

In this paper, we propose a reduced-form model to price default risk in mortgages and fixed-
rate pass-through mortgage-backed securities. Since the default of borrowers is often …

In this paper, we employ an intensity-based credit risk model with regime-switching to study
the valuation of basket CDS in a homogeneous portfolio. We assume that the default …

This current thesis aims to survey recent development on certain problems in Mathematical
Finance. The geometric Brownian motion model for stock price was rst proposed by the …