  This paper considers the optimal portfolio selection problem in a dynamic
multi-period stochastic framework with regime switching. The risk preferences
are of exponential (CARA) type with an absolute coefficient of risk aversion
which changes with the regime. The market model is incomplete and there are two
risky assets: one tradable and one non-tradable. In this context, the optimal
investment strategies are time inconsistent. Consequently, the subgame perfect
equilibrium strategies are considered. The utility indifference prices of a
contingent claim written on the risky assets are computed via an indifference
valuation algorithm. By running numerical experiments, we examine how these
prices vary in response to changes in model parameters.
