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STOCHASTIC DIFFERENTIAL GAMES BETWEEN TWO INSURERS WITH GENERALIZED MEAN-VARIANCE PREMIUM PRINCIPLE

Shumin Chen, Hailiang Yang, Yan Zeng
2018 ASTIN Bulletin: The Journal of the International Actuarial Association  
We study a stochastic differential game problem between two insurers, who invest in a financial market and adopt reinsurance to manage their claim risks.  ...  Supposing that their reinsurance premium rates are calculated according to the generalized mean-variance principle, we consider the competition between the two insurers as a non-zero sum stochastic differential  ...  also study the reinsurance game problem for two insurers under the assumption that the correlations between insurers are ambiguous.  ... 
doi:10.1017/asb.2017.35 fatcat:okbegmosfra4zimgszadztrimq

Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty

Xiangbo Meng, Ximin Rong, Lidong Zhang, Ziping Du
2016 Discrete Dynamics in Nature and Society  
In this paper, we study optimal investment-reinsurance strategies for an insurer who faces model uncertainty.  ...  The insurer is allowed to acquire new business and invest into a financial market which consists of one risk-free asset and one risky asset whose price process is modeled by a Geometric Brownian motion  ...  Different from those in Zhang and Siu [16] , we propose here a mean-variance portfolio optimization problem under model uncertainty. The rest of this paper is organized as follows.  ... 
doi:10.1155/2016/9693419 fatcat:7lpij3qbovfmvkyfwmecdn4plm

Page 1190 of Mathematical Reviews Vol. , Issue 89B [page]

1989 Mathematical Reviews  
Summary: “An agent can distribute his wealth between two in- vestements, one with a fixed rate of return r and the other with a random rate of return with mean r.  ...  The authors develop a model for two-candidate elections with a multidimensional policy space. The game-theoretic model includes both the candidates and the voters as players.  ... 

Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria

Bo Yi, Frederi Viens, Zhongfei Li, Yan Zeng
2014 Scandinavian Actuarial Journal  
some risk to a reinsurer, but worries about uncertainty in model parameters.  ...  uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout (2006) and Liu (2010).  ...  Recently, some scholars investigated optimal reinsurance and/or investment problems for insurers under utilities or mean-variance framework, including the use of the Black-Scholes framework for modeling  ... 
doi:10.1080/03461238.2014.883085 fatcat:teozbjwh3nfjrc47cxyombxt7q

Robust optimal investment and reinsurance of an insurer under Jump-diffusion models

Xin Zhang, Hui Meng, Jie Xiong, Yang Shen
2018 Mathematical Control and Related Fields  
This paper studies a robust optimal investment and reinsurance problem under model uncertainty. The insurer's risk process is modeled by a general jump process generated by a marked point process.  ...  By using the dynamic programming, we formulate the robust optimal investment and reinsurance problem into a two-person, zero-sum, stochastic differential game between the investor and the market.  ...  [36] considered robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria but only for a diffusion model without jump.  ... 
doi:10.3934/mcrf.2019003 fatcat:jwvgumjvbzbqrggac37wv4prv4

Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

Hanlei Hu, Zheng Yin, Xiujuan Gao
2018 Discrete Dynamics in Nature and Society  
The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated.  ...  The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer.  ...  [21] discuss the time-consistent reinsurance-investment strategy for two parties under a mean-variance framework. Cai et al.  ... 
doi:10.1155/2018/9424908 fatcat:brsuwujdv5hr5n7kderbuuusgy

Robust optimal control for an insurer with reinsurance and investment under Heston's stochastic volatility model

Bo Yi, Zhongfei Li, Frederi G. Viens, Yan Zeng
2013 Insurance, Mathematics & Economics  
This paper considers a robust optimal reinsurance and investment problem under Heston's Stochastic Volatility (SV) model for an Ambiguity-Averse Insurer (AAI), who worries about model misspecification  ...  We find that ignoring model uncertainty leads to significant utility loss for the AAI.  ...  For example, Bai & Guo (2008) and Zeng & Li (2011) studied the optimal reinsurance and investment strategies for insurers with mean-variance criteria.  ... 
doi:10.1016/j.insmatheco.2013.08.011 fatcat:lb2v5w2gajevjcx4pzz7ljvn6u

Alpha-robust investment-reinsurance strategy for a mean-variance insurer under a defaultable market [article]

Min Zhang, Yong He
2021 arXiv   pre-print
In this paper, we consider the robust optimal reinsurance investment problem of the insurer under the α-maxmin mean-variance criterion in the defaultable market.  ...  The insurer's surplus process is described by a Lévy insurance model.  ...  Under the 𝛼-maxmin mean variance criterion, we find the optimal reinsurance investment strategy with consistent time in the game theory framework.  ... 
arXiv:2112.04147v1 fatcat:vszsftz2ynagvbbrhadmp26bjm

Robust equilibrium investment and reinsurance strategy with bounded memory and common shock dependence

Sheng Li
2021 Reserche operationelle  
The insurer is assumed to be ambiguity-averse and make the optimal decision under the mean-variance criterion.  ...  In this paper, we consider the robust investment and reinsurance problem with bounded memory and risk co-shocks under a jump-diffusion risk model.  ...  Section 2 formulates the mean-variance investment and reinsurance problem with bounded memory and common shock dependence under model uncertainty.  ... 
doi:10.1051/ro/2021182 fatcat:7h6msn3hezennm27q36h4gjufy

PAPERS FROM ACTUARIAL JOURNALS WORLDWIDE

2013 Annals of Actuarial Science  
The model can also account for uncertainty in the marginal distributions.  ...  A prudent assessment of dependence is crucial in many stochastic models for insurance risks. Copulas have become popular to model such dependencies.  ...  Moreover, for two cases with or without a riskless asset, we obtain the time consistent analytical optimal investment policy and the mean-variance efficient frontier of the new model with the self-financing  ... 
doi:10.1017/s1748499513000055 fatcat:zq3otwnkxjcpbhqdb5mpjevgam

Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Jiaqi Zhu, Shenghong Li
2020 Mathematics  
This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market  ...  The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process.  ...  Zhu et al. (2019) [21] considered non-zero sum differential reinsurance and investment game between mean-variance insurers.  ... 
doi:10.3390/math8122183 fatcat:reqnrkizufgh5gcz4rrm6wvlzm

A hybrid stochastic differential reinsurance and investment game with bounded memory [article]

Yanfei Bai, Zhongbao Zhou, Helu Xiao, Rui Gao, Feimin Zhong
2019 arXiv   pre-print
This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum  ...  The two insurers, as the followers of the Stackelberg game, can purchase proportional reinsurance from the reinsurer and invest in the same financial market.  ...  Chen and Shen (2019) studied stochastic Stackelberg differential reinsurance games under time-inconsistent mean-variance framework.  ... 
arXiv:1910.09834v1 fatcat:htzt3ev6yne6zppxiwkhtzo7lm

PAPERS FROM ACTUARIAL JOURNALS WORLDWIDE

2015 Annals of Actuarial Science  
This paper is concerned with an optimal investment and reinsurance problem with delay for an insurer under the mean-variance criterion.  ...  Optimal investment-reinsurance with delay for mean-variance insurers: a maximum principle approach. 1-12.  ... 
doi:10.1017/s1748499514000323 fatcat:abz3p5cghvgmxhylgtxxfg5s6i

Underwriting in Property-Casualty Insurance Markets: Regulation, Risk and Volatility

Ronnie J. Phillips, David B. Nickerson
2011 Social Science Research Network  
Using a differential game in a standard no-arbitrage environment to model interaction between these two sources of risk, we derive the valuation equation for property-liability underwriting inclusive of  ...  We offer a novel explanation of underwriting volatility in propertyliability insurance markets in terms of private uncertainty over public regulatory policy.  ...  The reinsurer is under no obligation to accept the particular risk offered and the insurer is under no obligation to cede the particular risk.  ... 
doi:10.2139/ssrn.1911350 fatcat:7f44eou6k5b37b4zmsf3cng7uy

PAPERS FROM ACTUARIAL JOURNALS WORLDWIDE

2014 Annals of Actuarial Science  
Optimal proportional reinsurance and investment with regimeswitching for mean-variance insurers. 871-883.  ...  This work develops a stochastic differential game model between two insurance companies who adopt the optimal reinsurance strategies to reduce the risk.  ... 
doi:10.1017/s1748499514000207 fatcat:w6qlf5k6mjfo7pwqhjtoj4ufpy
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