Pessimistic Optimal Choice for Risk-Averse Agents

Abstract

We propose a general framework for the analysis of dynamic optimization with risk-averse agents, extending Whittle's (Whittle, 1990) formulation of risk-sensitive optimal control problems to accommodate time-discounting. We show how, within a Markovian set-up, optimal risk-averse behavior is identified via a pessimistic choice mechanism and described by simple recursive formulae. We apply this methodology to two distinct problems formulated respectively in discrete- and continuous-time. In the former, we extend Svensson's (Svensson, 1997) analysis of optimal monetary policy, showing that with a pessimistic central bank the inflation forecast is not longer an explicit intermediate target, the monetary authorities do not expect the inflation rate to mean revert to its target level and apply a more aggressive Taylor rule, while the inflation rate is less volatile. In the latter, we investigate the optimal production policy of a monopolistic entrepreneur which faces a demand schedule subject to stochastic shocks, once again showing that risk-aversion induces her to act more aggressively.