A Stochastic Maximum Principle and Cox, Ingersoll, Ross Interest Rate Model for an Optimal Investment under Partial Information

In this paper, we solve the problem of hedging of a European option.This is done by determining the optimal strategy for investing in the risky asset constituting the portfolio.We assume that the payoff of this contingent asset at maturity date does not only depend on the price of this risky asset to which it relates.But it also depends on an unobservable random variable .In addition to the risky asset, the portfolio for this hedging contains an asset whose price on each date before maturity is a deterministic function of a stochastic short-term interest rate .The dynamics of the process is that of the CIR (Cox, Ingersoll and Ross) model.which does not give negative values according to the parameters of the said model.We use classical filtering theory and stochastic partial differential equations (SPDE).Thus, we move from the partial information to the full information.Then, we use a stochastic maximum principle that we established with the backward stochastic differential equations (BSDE) to determine the optimal investment strategies and in the risky asset respectively in the presence of the option and in its absence.