Recursive Utility and Jump-Diffusions

We derive the equilibrium interest rate and risk premiums using recursive utility for jump-diffusions. Compared to to the continuous version, including jumps allows for a separate risk aversion related to jump size risk in addition to risk aversion related to the continuous part. The jump part also introduces moments of higher orders that may matter in many circumstances. 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. We demonstrate how the stochastic process for the market portfolio is determined in terms the corresponding processes for future utility and aggregate consumption. It is indicated that this model has the potential to give reasonable explanations of empirical puzzles