Hedging Security Portfolio with Random Parameters in Stochastic Linear Quadratic Framework

Adding European contingent claims to hedge the risk is important for controlling or decreasing the risk of portfolio, so this paper is concerned with the selection of continuous-time portfolio which include European contingent claims as a two-criteria optimization problems. Under mean-variance criteria, the objective is to maximize the expected terminal return and minimize the variance of final wealth of portfolio. Under the assumption of free transaction cost and of frictionless market, by martingale theorem the hedging strategy of portfolio is transformed into a single objective stochastic control problem which is however not in the standard problem and can be "embedded" into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an effective framework to study the mean-variance problem in the light of the recent development on general stochastic LQ problems. This paper provides with optimal dynamically hedging strategy of one kind of investment portfolio with random parameters in stochastic linear quadratic framework when equity derivatives were added to security portfolio. Then, the article has proved the existence of solution of Riccati equation.