Recursive utility and disappearing puzzles for continuous-time models

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. Two ordinally equivalent versions are considered. The state price is not Markov in any of the versions, so instead of using dynamic programming we use the stochastic maximum principle. The resulting equilibriums are consistent with low values of the parameters of the utility functions when calibrated to market data. One version is consistent with preference for early resolution of uncertainty, the other for late for the US-data. We therefore consider heterogeneity with recursive utilities. Our resulting model rationalize data well, and can explain both the Equity Premium Puzzle and the Risk-Free Rate Puzzle with good margins.