Explicit solutions for continuous time mean-variance portfolio selection with nonlinear wealth equations

摘要

This paper concerns the continuous time mean-variance portfolio selectionproblem with a special nonlinear wealth equation. This nonlinear wealthequation has a nonsmooth coefficient and the dual method developed in [6] doesnot work. We invoke the HJB equation of this problem and give an explicitviscosity solution of the HJB equation. Furthermore, via this explicitviscosity solution, we obtain explicitly the efficient portfolio strategy andefficient frontier for this problem. Finally, we show that our nonlinear wealthequation can cover three important cases.