FD-05: Optimal Control and Optimization in Economics, Finance and Management III
Stream: Optimal Control and Optimization in Economics, Finance and Management
Chair(s): Diogo Pinheiro
Stochastic Maximum Principle with Regimes and Memory
Emel Savku, Gerhard-Wilhelm Weber
We study a stochastic optimal control problem for a delayed Markov regime -switching jump-diffusion model. We establish necessary and sufficient maximum principles for such a system.We prove the existence– uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.
Portfolio Optimization with Drift Uncertainty
We study the utility maximization problem of a portfolio of one risky asset, a stock, and one riskless asset, a bond, under Knightian uncertainty on the drift term representing the long term growth rate of the risky asset. We further assume that the investor has a prior estimate about the drift term, so that we incorporate into the model a penalty term for deviating from the prior about the mean. We provide explicit solutions, when the investor has logarithmic, power and exponential utility functions.
Two-player zero-sum stochastic differential games with Markov-switching jump-diffusion dynamics
Diogo Pinheiro, Miguel Ferreira, Susana Pinheiro
We consider a two-player zero-sum stochastic differential game with Markov-switching jump-diffusion state variable dynamics. We study this game using a combination of dynamic programming and viscosity solution techniques. Under some mild assumptions, we prove that the value of the game exists and is the unique viscosity solution of a certain nonlinear partial integro-differential equation of Hamilton-Jacobi-Bellman-Isaacs type.