Asset and liability management for exponential utility preference in an incomplete market: The martingale approach

This paper is concerned with asset and liability management problem in an incomplete market from the viewpoints of expected utility maximization. The liability is supposed to be random process driven by Brownian motion with drift while risky assets' prices are governed by geometric Brownian motion. In addition, there exist correlations between the risky assets and the liability. The analytical optimal portfolios for exponential utility maximization are obtained by applying martingale approach.