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Terminal perturbation method for the backward approach to continuous time mean-variance portfolio selection. (English) Zbl 1152.60051

The authors are focused on developing the backward approach to continuous time mean-variance portfolio selection with nonlinear wealth equations in a complete market model. They introduce a new method, different from the Lagrange multiplier method, which is called the terminal perturbation method, to obtain the optimal terminal wealth in the first step. The terminal perturbation method is perturbing the terminal wealth directly to obtain a necessary condition which the optimal terminal wealth satisfies. More precisely,they perturb the terminal value of backward stochastic differential equation (BSDE) with initial constraint in which the terminal condition of the BSDE is regarded as the control “variable”. the main advantage of this method is that it can deal with some state constraints of the dynamic optimization problem easily. The authors introduce Ekeland’s variational principle to derive a stochastic maximum principle which characterizes the optimal terminal wealth.

MSC:

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