Explicit Representations for Utility Indifference Prices

Abstract

In this paper, we apply stochastic maximum principles to derive representations for exponential utility indifference prices. We also obtain the related optimal portfolio processes and utility indifference hedging strategies. To illustrate our theoretical results, we present several concrete examples and study the limit behavior of utility indifference prices for vanishing and infinite risk aversion. We further investigate how the optimal trading strategies and utility indifference prices alter, if one assumes that an investor has some additional information on the future behavior of the underlying stock price process available. In this regard, we propose a customized enlarged filtration approach and deduce a formula for the utility indifference price in this extended setup. We finally provide a representation for the information premium in our utility indifference pricing framework.