Continuous-time mean-variance portfolio selection: a stochastic LQ framework. (English) Zbl 0998.91023

Zhou, X. Y.; Li, D.

Appl. Math. Optimization 42, No. 1, 19-33 (2000).

This paper studies the continuous-time mean-variance portfolio selection problem of finding a self-financing portfolio strategy with maximal mean and minimal variance of terminal wealth. The model for the financial market has one riskless and \(m\) risky assets driven by an \(m\)-dimensional Brownian motion; all coefficients are deterministic and sufficiently regular so that one has a complete market. The main idea is to embed this problem into a class of auxiliary stochastic Linear-Quadratic (LQ) control problems with a single objective. The authors show how these can be solved by solving a suitable pair of ODEs and determine the efficient frontier for the original mean-variance problem. An interesting feature of the considered LQ problems is that the weight for the running cost is indefinite.

Reviewer: Martin Schweizer (München)

MSC:

91G10	Portfolio theory
93E20	Optimal stochastic control

Keywords:

mean-variance analysis; linear-quadratic control; portfolios; efficient frontier