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.
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)
Acknowledgements
The authors gratefully acknowledge the Editor and two anonymous referees for their insightful comments and helpful suggestions that led to a marked improvement of the article.
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Articles in the same Issue
- A High-Moment Trapezoidal Fuzzy Random Portfolio Model with Background Risk
- Sequential First-Price Auction with Randomly Arriving Buyers
- Worst-Case Investment Strategy with Delay
- Research on Advertising and Pricing in E-Supply Chain Under Different Dominant Modes
- Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations
- Optimal Insurance-Package and Investment Problem for an Insurer