Multi-objective optimal control of stochastic hybrid systems

We present a dynamic programming based solution to a stochastic optimal control problem for a controlled discrete-time stochastic hybrid system. A general summultiplicative cost function is introduced along with a corresponding dynamic recursion that quantifies the weighted costs of achieving multiple (possibly competing) objectives relevant to the theory of stochastic verification and stochastic model predictive control. It is shown that a valuable collection of multi-objective stochastic optimal control problems can be expressed in the form of the presented general sum-multiplicative cost function. A case study in the early retirement problem (equivalently the reinsurance problem) is presented.