In this problem, the optimal path is one that maximizes the expected utility, with the utility function being piecewise-linear and concave. Such a utility function can be used to approximate nonlinear ...

Laurence Carassus, Miklós Rásonyi, Maximization of Nonconcave Utility Functions in Discrete-Time Financial Market Models, Mathematics of Operations Research, Vol. 41, No. 1 (February 2016), pp.