Pessimistic Optimal Choice for Risk-averse Agents: The Continuous-time Limit

We extend Hansen and Sargent’s (Hansen and Sargent, 1994, 1995, 2005) analysis of dynamic optimization with risk-averse agents in two directions. Firstly, following Whittle (Whittle, 1990), we show that the optimal risk-averse policy is identified via a pessimistic choice mechanism and described by simple recursive formulae. Secondly, we investigate the continuous-time limit and show that sufficient conditions for the existence of optimal solutions coincide with those which apply under risk-neutrality. Our analysis is conducted both under perfect and imperfect state observation. As an illustrative example, we analyze the optimal production policy of an entrepreneur running a monopolistic firm which faces a demand schedule subject to stochastic shocks, showing that risk-aversion induces her to act more aggressively.