Abstract
In this work we consider a continuous-time mean-variance portfolio selection problem that is formulated as a bi-criteria optimization problem. The objective is to maximize the expected return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form. We show that this non-standard problem can be “embedded” into a class of auxiliary stochastic linear-quadratic (LQ) problems. By solving the latter based on the recent development on stochastic LQ problems with indefinite control weighting matrices, we derive the efficient frontier in a closed form for the original mean-variance problem.
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