Risk-averse Merton’s Portfolio Problem

摘要

A one-dimensional version of a continuous-time Merton’s portfolio problem is solved numerically for different cost functionals involving the probability distribution of the state variable. Such functionals allow to take into account the risk aversion of the consumer. The associated optimality conditions consist in a coupled system of the Fokker-Planck and the Hamilton-Jacobi-Bellman equations, as is customary for mean-field type optimal control problems. We solve this coupled system with an iterative method.