Optimal investment with derivatives and pricing in an incomplete market

Abstract

This paper investigates the optimal investment strategy and the pricing of derivatives in an incomplete financial market with one risk-free asset, one stock and one non-redundant derivative security. In the exponential utility maximization criterion, a dynamic relationship between optimal positions for the stock and derivative security is established and the dynamic derivatives pricing formulae depending on the current optimal positions are also obtained by employing the stochastic control approach. The explicit representations of the corresponding solutions are demonstrated and their properties are discussed. Finally, numerical results are presented to characterize the behavior of the derivative security price.