1.Department of Mathematics,Rutgers University,Piscataway,USA;2.Department of Mathematics,University of Connecticut,Storrs,USA;3.Department of Mathematics,University of Texas at Austin,Austin,USA
Abstract:
In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.