Risk Aware Minimum Principle for Optimal Control of Stochastic Differential Equations

We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions which the neutral expectation replaced function, nonlinear functional random variables that accounts controller's preferences. state and prove minimum principle gives necessary sufficient conditions optimality generalized processes taking values on probability measures defined given action space. show going from to case, modified introduction one additional real-valued process acts as adjustment factor. This explicitly expectation, conditional filtration at time, an appropriately derivative function evaluated total cost. The model we employ differs standard relaxed controls, elaborate differences, benefits drawbacks, types; further give under can be realized using strict process. application results portfolio allocation problem rise premium term characterized described above. suggests uses e.g. pricing modeled generic financial applications.