Recursive utility and jump-diffusions

Abstract

We consider agents in an exchange economy having preferences represented by scale invariant recursive utility, where the dynamics of both consumption and risky assets are given by jump-diffusions. In this setting we find state prices, where both diffusion and jump-size risk are priced. By including jumps, the theory has the potential to model insurance markets, as well as ordinary securities’ markets. In the latter case, we derive the equilibrium, real interest rate and risk premiums. In the former case we consider catastrophe futures related to negative shocks in consumption. We use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations, and seems indispensable in this theory.