Asset-liability Problem With Mean-variance Preferences And Constraints

Risk assets portfolio problem need to solve above all is the two contents: expectedreturn and risk. How to measure portfolio risk and return and how to balance these twomeans standard asset allocation need to be addressed urgently for the problem of marketinvestors. This thesis is devoted to mean-variance portfolio selection problem in in contin-uous time financial markets, where the objective is to minimize the risk of the investmentwhich is expressed by the variance of the terminal wealth and at the same to maximizethe expected terminal return. Two main problem are considered under continuous timemean-variance framework:First of all, this paper deals with mean-variance portfolio asset-liability problems underthe constraint that short-selling of stocks is prohibited. Risk securities and debt in Marketis described with difusion process. First, the problem is formulated as a stochastic optimallinear-quadratic(LQ) control problem as an auxiliary problem of the initial problem, and averification theorem for general stochastic optimal control is showed. Then by applying theverification theorem and solving the HJB equation, the optimal strategies in an explicitform for the auxiliary and initial control problem are presented, at the same time theefcient frontier in a closed form for the initial problem is derived.Secondly, this paper deals with asset-liability problems follow an jump-difusion pro-cess. First, the problem is formulated as a stochastic optimal linear-quadratic(LQ) controlproblem, a continuous function is constructed via two Riccati equations, and then it isshown that this function is a viscosity solution to the HJB equation, then by solving theseRiccati equation enables one to explicitly obtain the optimal investment strategies andefcient frontier for the original mean-variance problem.