OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM WITH CONSTRAINTS ON RISK CONTROL IN A GENERAL JUMP-DIFFUSION FINANCIAL MARKET

被引：5

作者：

Zhu, Huiming ^{[1
]}

Huang, Ya ^{[1
]}

Zhou, Jieming ^{[2
]}

Yang, Xiangqun ^{[2
]}

Deng, Chao ^{[1
]}

机构：

[1] Hunan Univ, Coll Business Adm, Changsha 410082, Hunan, Peoples R China

[2] Hunan Normal Univ, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China

来源：

ANZIAM JOURNAL | 2016年 / 57卷 / 03期

基金：

中国国家自然科学基金;

关键词：

jump-diffusion risk model; optimal investment strategy; proportional reinsurance; exponential utility; Hamilton-Jacobi-Bellman equation; EXPONENTIAL UTILITY; OPTIMAL PORTFOLIO; RUIN PROBABILITY; INSURER; ASSETS; MODEL;

D O I：

10.1017/S1446181115000280

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer's surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.

引用

页码：352 / 368

页数：17

共 50 条

[31] RISK MANAGEMENT OF FINANCIAL CRISES: AN OPTIMAL INVESTMENT STRATEGY WITH MULTIVARIATE JUMP-DIFFUSION MODELS
Wang, Chou-Wen
Huang, Hong-Chih
[J]. ASTIN BULLETIN, 2017, 47 (02): : 501 - 525
[32] Dynamic optimal portfolio choice in a jump-diffusion model with investment constraints
Jin, Xing
Zhang, Kun
[J]. JOURNAL OF BANKING & FINANCE, 2013, 37 (05) : 1733 - 1746
[33] OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT IN JUMP DIFFUSION MARKETS WITH NO SHORT-SELLING AND NO BORROWING
Zhang Jingxiao
Cao Kai
Kannan, D.
[J]. DYNAMIC SYSTEMS AND APPLICATIONS, 2015, 24 (1-2): : 169 - 185
[34] Optimal Mean-Variance Problem with Constrained Controls in a Jump-Diffusion Financial Market for an Insurer
Bi, Junna
Guo, Junyi
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 157 (01) : 252 - 275
[35] Optimal Mean-Variance Problem with Constrained Controls in a Jump-Diffusion Financial Market for an Insurer
Junna Bi
Junyi Guo
[J]. Journal of Optimization Theory and Applications, 2013, 157 : 252 - 275
[36] THEORETICAL ANALYSIS FOR OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM
Zhang, Xinli
Sun, Wenyu
[J]. PACIFIC JOURNAL OF OPTIMIZATION, 2012, 8 (03): : 517 - 531
[37] OPTIMAL REINSURANCE AND INVESTMENT FOR A JUMP DIFFUSION RISK PROCESS UNDER THE CEV MODEL
Lin, Xiang
Li, Yanfang
[J]. NORTH AMERICAN ACTUARIAL JOURNAL, 2011, 15 (03) : 417 - 431
[38] Optimal portfolio selection in a jump-diffusion market with both fixed and proportional transaction costs
Deng, Guohe
[J]. PROCEEDINGS OF 2008 INTERNATIONAL CONFERENCE ON SYSTEM MANAGEMENT, 2008, : 346 - 354
[39] Finite Horizon Optimal Dividend and Reinsurance Problem Driven by a Jump-Diffusion Process with Controlled Jumps
Guan, Chonghu
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2023, 88 (01):
[40] Finite Horizon Optimal Dividend and Reinsurance Problem Driven by a Jump-Diffusion Process with Controlled Jumps
Chonghu Guan
[J]. Applied Mathematics & Optimization, 2023, 88

← 1 2 3 4 5 →