A Regime-Switching Model with Applications to Finance: Markovian and Non-Markovian Cases

A Markov regime-switching model may capture abrupt changes in the financial market efficiently, which are generated by inner or outer effects in an economy. These systems are governed by both continuous and discrete time dynamics, for which they are also called hybrid systems and have many applications in science and technology. In this work, we present a survey of financial applications under a specific semimartingale result of Markov chains. First, we present a robust portfolio strategy, which is also a zero-sum stochastic differential game. Second, optimal portfolio formulas of two investors’ collaboration are established by a nonzero-sum game. Both of these applications are solved by the Dynamic Programming Principle (DPP) approach in stochastic games. Our third result is an optimal consumption problem of a cash flow with regimes and time delay. This last financial problem is represented by the results of the necessary and sufficient stochastic Maximum Principle (MP).