Tomasz Bielecki
(Department of Mathematics, Northeastern Illinois University)
Continuous-Time Mean-Variance Portfolio Selection with Bankrupcty Prohibition
Abstract
A continuous-time Markowitz's mean-variance portfolio selection problem
is studied where all the market coefficients are random and the wealth
process under any admissible portfolio is not allowed to be below zero
at any time. Feasibility of the problem is first characterized. Then, after
having solved a system of algebraic equations, minimum variance portfolios
are derived as the replicating portfolios of some contingent claims, and
the minimum variance frontier is obtained. In the special case where the
market coefficients are deterministic, more explicit results are obtained.
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