Minimum probability function of crossing the upper regulatory threshold for asset-liability management

Abstract

In this paper, a stochastic model of asset-liability multiple is considered. To avoid the unbearable investment risk of asset price collapse, an upper regulatory threshold constraint is imposed on the asset-liability multiple. A Hamilton-Jacobi-Bellman (HJB) equation is established using the stochastic optimal control technique. The explicit minimum probability function and the optimal investment strategy are obtained, meanwhile, a verification theorem is also proved. Numerical examples illustrate the effectiveness of our results, which indicates that the current level and the upper regulatory threshold have significant influences on the minimum probability function.

Keywords:

• Asset-liability multiple
• upper regulatory threshold
• minimum probability function

Acknowledgments

The authors are deeply indebted to professor Bin Li in department of statistics and Actuarial Science of University of Waterloo for his very helpful comments and valuable suggestions.

Additional information

Funding

This research was supported by China Postdoctoral Science Foundation funded project (Grant No. 2017M611192), Youth Science Fund of Shanxi University of Finance and Economics (Grant No. QN-2017019). This work was also supported by the National Natural Science Foundation of China (No. 11801179), the “Chenguang Program”, Shanghai, China (No. 18CG26), the Fundamental Research Funds for the Central Universities (No. 2019ECNU-HWFW028), the 111 Project, China (No. B14019).