Hedging in incomplete markets and optimal control
نویسندگان
چکیده
We consider a problem of Duffie and Richardson in an economy in which there are two observable processes X and Y both driven by Brownian motions. One of processes is the price process of the asset which can be used for hedging the contingent claim. The objective is to find a trading strategy which minimizes the deviation (in p-norm or other loss function) of the portfolio value from the stochastic liability (contingent claim). We solve this problem in the framework of stochastic control. Introducing a new coordinate equal to the value of the portfolio we write the Hamilton-Jacobi-Bellman equation, which is a nonlinear partial differential equation in three variables.We give a solution to this equation in special cases and find the optimal hedging policy.
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