Mixture dynamics and regime switching diffusions with application to option pricing (Q539521)

The goal of this paper is to develop a mixture dynamics in a regime-switching diffusion framework. This class of models is described by a pair \((X(t), Y(t)) \in \mathbb R^n \times {\mathcal S}\), \({\mathcal S} = \{1,2,\dots, N \}\), \(Y(t)\) being a Markov chain for which the marginal probability of the diffusive component \(X(t)\) is a given mixture. While in many applications the Markov chain is independent from the diffusive component, the novelty is that here a state dependent regime-switching framework is considered to get an explicit mixture dynamics. A simple algorithm for simulating paths through a thinning mechanism is proposed, and an application to option pricing is discussed.