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 ...

Niels Erik Jensen, An Introduction to Bernoullian Utility Theory: I. Utility Functions, The Swedish Journal of Economics, Vol. 69, No. 3 (Sep., 1967), pp. 163-183 ...