Optimal investment and risk control policies for an insurer in an incomplete market

被引：9

作者：

Zhou, Jieming ^{[1
,2
]}

Zhang, Xiaoye ^{[1
]}

Huang, Ya ^{[3
]}

Xiang, Xuyan ^{[2
]}

Deng, Yingchun ^{[1
,2
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, Minist Educ, LCSM, Changsha, Hunan, Peoples R China

[2] Hunan Univ Arts & Sci, Sch Math & Phys, Hunan Prov Cooperat Innovat Ctr Construct & Dev, Changde, Hunan, Peoples R China

[3] Hunan Normal Univ, Sch Business, Changsha, Hunan, Peoples R China

来源：

OPTIMIZATION | 2019年 / 68卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Investment; risk control; martingale approach; mean-variance; expected utility; OPTIMAL PROPORTIONAL REINSURANCE; ROBUST OPTIMAL INVESTMENT; LEVY MARKET; MARTINGALE; PORTFOLIO; UTILITY; MODEL;

D O I：

10.1080/02331934.2019.1581778

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we apply the martingale approach to investigate the optimal investment and risk control problem for an insurer in an incomplete market. The claim risk of per policy is characterized by a compound Poisson process with drift, and the insurer can be invested in multiple risky assets whose price processes are described by the geometric Brownian motions model. By 'complete' the incomplete market, closed-form solutions to the problems of mean-variance criterion and expected exponential utility maximization are obtained. Moreover, numerical simulations are presented to illustrate the results with the basic parameters.

引用

页码：1625 / 1652

页数：28

共 30 条

[1]

[Anonymous], CRC FINANCIAL MATH S

[2] Optimal control and dependence modeling of insurance portfolios with Levy dynamics [J].

Baeuerle, Nicole ;

Blatter, Anja .

INSURANCE MATHEMATICS & ECONOMICS, 2011, 48 (03) :398-405

[3] Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint [J].

Bai, Lihua ;

Guo, Junyi .

INSURANCE MATHEMATICS & ECONOMICS, 2008, 42 (03) :968-975

[4] Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin [J].

Browne, S .

MATHEMATICS OF OPERATIONS RESEARCH, 1995, 20 (04) :937-958

[5] OPTIMAL CONSUMPTION AND PORTFOLIO POLICIES WHEN ASSET PRICES FOLLOW A DIFFUSION PROCESS [J].

COX, JC ;

HUANG, CF .

JOURNAL OF ECONOMIC THEORY, 1989, 49 (01) :33-83

[6] On optimal investment in a reinsurance context with a point process market model [J].

Edoli, Enrico ;

Runggaldier, Wolfgang J. .

INSURANCE MATHEMATICS & ECONOMICS, 2010, 47 (03) :315-326

[7] Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model [J].

Gu, Ailing ;

Guo, Xianping ;

Li, Zhongfei ;

Zeng, Yan .

INSURANCE MATHEMATICS & ECONOMICS, 2012, 51 (03) :674-684

[8] Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks [J].

Guan, Guohui ;

Liang, Zongxia .

INSURANCE MATHEMATICS & ECONOMICS, 2014, 55 :105-115

[9] MARTINGALES AND ARBITRAGE IN MULTIPERIOD SECURITIES MARKETS [J].

HARRISON, JM ;

KREPS, DM .

JOURNAL OF ECONOMIC THEORY, 1979, 20 (03) :381-408

[10] Robust optimal investment and reinsurance problem for the product of the insurer's and the reinsurer's utilities [J].

Huang, Ya ;

Ouyang, Yao ;

Tang, Lingxiao ;

Zhou, Jieming .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 344 :532-552

← 1 2 3 →