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Worst-Case Investment Strategy with Delay

Author

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  • A Chunxiang

    (School of Mathematics and Statistics, Zhaoqing University, Guangdong, 526061, China)

  • Shao Yi

    (School of Mathematics and Statistics, Zhaoqing University, Guangdong, 526061, China)

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.

Suggested Citation

  • A Chunxiang & Shao Yi, 2018. "Worst-Case Investment Strategy with Delay," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 35-57, February.
    • Handle: RePEc:bpj:jossai:v:6:y:2018:i:1:p:35-57:n:3
    DOI: 10.21078/JSSI-2018-035-23
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    References listed on IDEAS

    as
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