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Optimal portfolio selection when stock prices follow an jump-diffusion process. (English) Zbl 1123.91026
The authors are dealing with a portfolio selection problem in which the stock prices follow a jump-diffusion process by using a mean-variance analysis approach. The basic idea here is to introduce a stochastic linear-quadratic (LQ) control problem which goes back to X. Y. Zhou and D. Li [Appl. Math. Optimization 42, 19–33 (2000; Zbl 0998.91023)]. To this end, the authors derive a verification theorem for general stochastic optimal control problems in which the states follow a jump-diffusion process. This, in turn, is used to solve the HJB equation corresponding to the LQ problem.

MSC:
91G10 Portfolio theory
60J60 Diffusion processes
60J75 Jump processes (MSC2010)
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