  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.
