Advances in optimal control of markov regime-switching models with applications in finance and economics

Savku, Emel
We study stochastic optimal control problems of finance and economics in a Markov regime-switching jump-diffusion market with and without delay component in the dynamics of our model. We formulate portfolio optimization problems as a two player zero-sum and a two player nonzero-sum stochastic differential games. We provide an extension of Dynkin formula to present the Hamilton-Jacobi-Bellman-Isaacs equations in such a more general setting. We illustrate our results for a nonzero-sum stochastic differential game and investigate the impact of regime-switches by comparative statics of a two state Markov regime-switching jump-diffusion model. We prove the existence-uniqueness theorems for a stochastic differential delay equation with jumps and regimes (SDDEJR) and for an anticipated backward stochastic differential equation with jumps and regimes (ABSDEJR). Furthermore, we give the duality between an SDDEJR and an ABSDEJR. We establish necessary and sufficient maximum principles under full and partial information for an SDDEJR. We show that the adjoint equations are represented by an ABSDEJR. We apply our results to a problem of optimal consumption problem from a cash flow with delay and regimes.