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Dual method for continuous-time Markowitz’s problems with nonlinear wealth equations. (English) Zbl 1220.91034

Summary: Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal wealth and portfolio is the solution of a forward-backward stochastic differential equation with constraints.

MSC:

91G10 Portfolio theory
93E20 Optimal stochastic control
60H30 Applications of stochastic analysis (to PDEs, etc.)
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