Abstract
Both necessary and sufficient maximum principles for optimal control of stochastic system with random jumps consisting of forward and backward state variables are proved. The control variable is allowed to enter both diffusion and jump coefficients. The result is applied to a mean-variance portfolio selection mixed with a recursive utility functional optimization problem. Explicit expression of the optimal portfolio selection strategy is obtained in the state feedback form.
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This research is supported by the National Basic Research Program of China (973 Program) under Grant No. 2007CB814904, the National Natural Science Foundations of China under Grant Nos. 10921101 and 10701050, and the Natural Science Foundation of Shandong Province under Grant Nos. JQ200801 and 2008BS01024.
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Shi, J., Wu, Z. Maximum principle for forward-backward stochastic control system with random jumps and applications to finance. J Syst Sci Complex 23, 219–231 (2010). https://doi.org/10.1007/s11424-010-7224-8
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DOI: https://doi.org/10.1007/s11424-010-7224-8