Recursive utility using the stochastic maximum principle

Abstract

Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous time model. We consider the version of recursive utility which gives the most unambiguous separation of risk preference from time substitution, and use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations. With existence granted, the market portfolio is determined in terms of future utility and aggregate consumption in equilibrium. The equilibrium real interest rate is also derived, and the the model is shown to be consistent with reasonable values of the parameters of the utility function when calibrated to market data, under various assumptions.s that the state prices depend on past consumption. We use the stochastic maximum principle and forward/backward stochastic di erential equations to derive two ordinally equivalent versions. The resulting equilibrium is consistent with reasonable values of the parameters of the utility functions when calibrated to market data, under various assumptions.