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Zbl 0998.91023
Zhou, X.Y.; Li, D.
Continuous-time mean-variance portfolio selection: A stochastic LQ framework. (English)
[J] Appl. Math. Optimization 42, No.1, 19-33 (2000). ISSN 0095-4616; ISSN 1432-0606/e

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.
[Martin Schweizer (München)]

MSC 2000:: *91B28 Finance etc.
93E20 Optimal stochastic control (systems)

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

Cited in: Zbl 1207.60041 Zbl 1184.93121 Zbl 1182.91161 Zbl 1123.91026

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