In this paper, we propose an equilibrium pricing model in a dynamic
multi-period stochastic framework with uncertain income streams. In an
incomplete market, there exist two traded risky assets (e.g. stock/commodity
and weather derivative) and a non-traded underlying (e.g. temperature). The
risk preferences are of exponential (CARA) type with a stochastic coefficient
of risk aversion. Both time consistent and time inconsistent trading strategies
are considered. We obtain the equilibriums prices of a contingent claim written
on the risky asset and non-traded underlying. By running numerical experiments
we examine how the equilibriums prices vary in response to changes in model
parameters.