Stability of numerical methods for jump diffusions and Markovian switching jump diffusions

Numerical methods for controlled regime-switching diffusions and regime-switching jump diffusions

This work is concerned with numerical methods for controlled regime-switching diffusions, and regime-switching jump diffusions. Numerical procedures based on Markov chain approximation techniques are developed. Convergence of the algorithms is derived by means of weak convergence methods. In addition, examples are also provided for demonstration purpose. 2006 Elsevier Ltd. All rights reserved.

Numerical solutions for jump-diffusions with regime switching

This paper is devoted to numerical solutions for a class of jump-diffusions with regime switching. After briefly reviewing the notion of jump-diffusions with regime switching, finite-difference procedures are constructed. Under simple conditions, it is proved that the algorithm converges to the desired limit by means of a martingale problem formulation. Numerical experiments are carried out to ...

First Passage Time Moments of Jump-Diffusions with Markovian Switching

Option Pricing in Some Non-Lévy Jump Models

This paper considers pricing European options in a large class of one-dimensional Markovian jump processes known as subordinate diffusions, which are obtained by time changing a diffusion process with an independent Lévy or additive random clock. These jump processes are nonLévy in general, and they can be viewed as natural generalization of many popular Lévy processes used in finance. Subordin...

Singular stochastic control and optimal stopping with partial information of jump diffusions

We study partial information, possibly non-Markovian, singular stochastic control of jump diffusions and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected BSDEs and optimal stopping in the partial information case. Mathematics Subject Classification 2010: 93E20, 60H07, 60H10, 60HXX, 60J75