Mean-Variance Asset Liability Management with State-Dependent Risk Aversion |
| |
Authors: | Yan Zhang Shuang Li Benchawan Wiwatanapataphee |
| |
Institution: | 1. Department of Mathematics, Faculty of Science, Mahidol University, Centre of Excellence in Mathematics, Commission on Higher Education, Bangkok, Thailand;2. Department of Mathematics and Statistics, Curtin University, Bentley Campus, Perth, Australia |
| |
Abstract: | This article investigates the asset liability management problem with state-dependent risk aversion under the mean-variance criterion. The investor allocates the wealth among multiple assets including a risk-free asset and multiple risky assets governed by a system of geometric Brownian motion stochastic differential equations, and the investor faces the risk of paying uncontrollable random liabilities. The state-dependent risk aversion is taken into account in our model, linking the risk aversion to the current wealth held by the investor. An extended Hamilton-Jacobi-Bellman system is established for the optimization of asset liability management, and by solving the extended Hamilton-Jacobi-Bellman system, the analytical closed-form expressions for the time-inconsistent optimal investment strategies and the optimal value function are derived. Finally, numerical examples are presented to illustrate our results. |
| |
Keywords: | |
|
|