Markov perfect equilibria in stochastic growth models with quasi-hyperbolic discounting and risk-sensitive preferences

We show the existence of a Markov perfect equilibrium in a non-stationary stochastic growth model with quasi-hyperbolic discounting and risk-sensitive preferences. Our proof resembles dynamic programming approach and does not involve any fixed point theorem. The risk-sensitive preferences are modelled via certainty equivalents for various utility functions including these implying risk-aversion as well as risk-seeking. Under the additional assumption of stationarity, we are able to prove the existence of a stationary Markov perfect equilibrium using the Schauder fixed point theorem.