A FREE BOUNDARY PROBLEM OF LIQUIDITY MANAGEMENT FOR OPTIMAL DIVIDEND AND INSURANCE IN FINITE HORIZON

被引：2
|
作者：
Chen, Xiaoshan [1 ]
Guan, Chonghu [2 ]
Yi, Fahuai [1 ]
机构：
[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
[2] Jiaying Univ, Dept Math, Meizhou 514015, Peoples R China
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2021年 / 59卷 / 04期
关键词：
Barenblatt equation; gradient constraint; free boundary; stochastic control;
D O I：
10.1137/20M1329949
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we devote our attention to the liquidity and risk management of a firm who faces two types of risks: a Poisson risk that can be insured for a fair premium and a Brownian risk that cannot be hedged nor insured. We apply a PDE method to solve this problem; the associated HJB equation is a Barenblatt equation with a gradient constraint in finite horizon. We not only show the existence of a classical solution to the problem, but also characterize the properties of the free boundaries arising from the HJB equation; especially, we are able to give a sufficient and necessary condition for the existence of the insurance free boundary.
引用
收藏
页码：2524 / 2545
页数：22
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