Worst-Case Investment Strategy with Delay

A Chunxiang () and Shao Yi ()
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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

Journal of Systems Science and Information, 2018, vol. 6, issue 1, 35-57

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.

Keywords: worst-case scenario; portfolio; stochastic differential delay equation; Hamilton-Jacobi-Bellman equation; equilibrium strategies (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/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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