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

##### MSC:
 91B28 Finance etc. (MSC2000) 93E20 Optimal stochastic control (systems)