Worst-Case Investment Strategy with Delay
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Journal of Systems Science and Information  2018, Vol. 6 Issue (1): 35-57    DOI: 10.21078/JSSI-2018-035-23
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Worst-Case Investment Strategy with Delay
Chunxiang A, Yi SHAO
School of Mathematics and Statistics, Zhaoqing University, Guangdong 526061, China
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Abstract This paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.
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Chunxiang A
Key wordsworst-case scenario   portfolio   stochastic differential delay equation   Hamilton-JacobiBellman equation   equilibrium strategies     
Received: 2017-01-05;
Fund: Supported by the National Natural Science Foundation of China (71501050), Startup Foundation for Doctors of ZhaoQing University (611-612282) and the National Science Foundation of Guangdong Province of China (2017A030310660)
Cite this article:   
Chunxiang A,Yi SHAO. Worst-Case Investment Strategy with Delay[J]. Journal of Systems Science and Information, 2018, 6(1): 35-57.
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