Stochastic Optimal Growth Model with Risk Sensitive Preferences

TL;DR

This paper develops a stochastic optimal growth model incorporating risk-sensitive preferences, proving the existence of a stationary optimal policy and deriving the associated Euler equation under unbounded shocks and utility.

Contribution

It introduces a novel framework for growth models with risk-sensitive preferences and unbounded shocks, establishing existence and optimality conditions.

Findings

Existence of a stationary optimal policy under risk-sensitive preferences.

Derivation of the Euler equation incorporating the optimality condition.

Validation of the optimality equation for unbounded productivity shocks.

Abstract

This paper studies a one-sector optimal growth model with i.i.d. productivity shocks that are allowed to be unbounded. The utility function is assumed to be non-negative and unbounded from above. The novel feature in our framework is that the agent has risk sensitive preferences in the sense of Hansen and Sargent (1995). Under mild assumptions imposed on the productivity and utility functions we prove that the maximal discounted non-expected utility in the infinite time horizon satisfies the optimality equation and the agent possesses a stationary optimal policy. A new point used in our analysis is an inequality for the so-called associated random variables. We also establish the Euler equation that incorporates the solution to the optimality equation.