  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.
