Regime switching optimal growth model with risk sensitive preferences

Anindya Goswami, Nimit Rana, Tak Kuen Siu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider a risk-sensitive optimization of consumption-utility on an 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 independent and identically distributed (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 a joint stationary distribution of the optimal growth process and the underlying regime process is examined. Finally, we present a numerical solution by considering a power utility and some hypothetical values of parameters in a regime switching extension of the Cobb–Douglas production rate function.
Original languageEnglish
Article number102702
Pages (from-to)1-18
Number of pages18
JournalJournal of Mathematical Economics
Volume101
DOIs
Publication statusPublished - Aug 2022

Keywords

  • Regime switching models
  • Growth models
  • Risk sensitive preferences
  • Optimal consumption
  • Euler equation

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