2015/08/21 by Andrzej Ruszczynski, Ruszczynski, Andrzej, Jianing Yao +1
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1508.05316
arxiv created 2016/08/19 · arxiv updated 2016/08/22
We consider optimal control problems for diffusion processes, where the objective functional is defined by a time-consistent dynamic risk measure. We focus on coherent risk measures defined by g-evaluations. For such problems, we construct a family of time and space perturbed systems with piecewise-constant control functions. We obtain a regularized optimal value function by a special mollification procedure. This allows us to establish a bound on the difference between the optimal value functions of the original problem and of the problem with piecewise-constant controls.