First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems

In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints whose costs are general, possibly nonsmooth finite coherent risk measures. Unlike preexisting contributions covering situation, our analysis holds classical differential equations driven by standard Brownian motions. addition, it presents the advantages of neither involving second-order adjoint nor leading so-called weak version maximum principle, in which maximization condition with respect variable is replaced stationarity Hamiltonian.