Regime Switching Optimal Growth Model with Risk Sensitive Preferences

TL;DR

This paper develops a regime-switching optimal growth model incorporating risk-sensitive preferences, establishing existence, uniqueness, and stationarity of solutions, and providing a numerical example with power utility and regime-dependent production functions.

Contribution

It introduces a comprehensive framework for risk-sensitive growth models with regime switching, proving key properties and deriving the Euler equation for optimal consumption.

Findings

Existence and uniqueness of the value function under regime switching.

Optimal policies are stationary and exist within a specific class.

Numerical illustration with power utility and regime-dependent Cobb-Douglas production.

Abstract

We consider a risk-sensitive optimization of consumption-utility on infinite time horizon where the one-period investment gain depends on an underlying economic state whose evolution over time is assumed to be described by a discrete-time, finite-state, Markov chain. We suppose that the production function also depends on a sequence of i.i.d. random shocks. For the sake of generality, the utility and the production functions are allowed to be unbounded from above. Under the Markov regime-switching model, it is shown that the value function of optimization problem satisfies an optimality equation and that the optimality equation has a unique solution in a particular class of functions. Furthermore, we show that an optimal policy exists in the class of stationary policies. We also derive the Euler equation of optimal consumption. Furthermore, the existence of the unique joint stationary distribution of the optimal growth process and the underlying regime process is examined. Finally, we present a numerical solution by considering power utility and some hypothetical values of parameters in a regime switching extension of Cobb-Douglas production rate function.