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Uniform Asymptotics for finite-time ruin probability in a Dependent Risk Model with General Stochastic Investment Return Process

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Acta Mathematicae Applicatae Sinica 2021年第4期37卷 847-857页

作者： Yang YANG Kam Chuen YUEN Jun-feng LIU School of Statistics and Data Science Nanjing Audit UniversityNanjing211815China Department of Statistics and Actuarial Science The University of Hong KongPokfulam RoadHong KongChina

In this paper,we consider a non-standard renewal risk model with dependent claim sizes,where an insurance company is allowed to invest his/her wealth in financial assets,leading to some stochastic investment log-returns described as a general adapted càdlàg *** the assumptions that the claim sizes are heavy-tailed and the stochastic log-return process on investments is bounded from below almost surely,we derive some asymptotic formulas for the finite-time ruin probability holding uniformly in any finite time horizon.

关键词： finite-time ruin probability stochastic log-return process on investments upper tail asymptotic independence dominated variation uniformity

Estimates for the finite-time ruin probability with Insurance and Financial Risks

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Acta Mathematicae Applicatae Sinica 2012年第4期28卷 795-806页

作者： Min ZHOU Kai-yong WANG Yue-bao WANG Department of Mathematics Soochow University Beijing Normal University-Hongkong Baptist University United International College School of Mathematics and Physics Suzhou University of Science and Technology

The paper gives estimates for the finite-time ruin probability with insurance and financial risks. When the distribution of the insurance risk belongs to the class L（γ） for some γ〉0 or the subexponential distribution class, we abtain some asymptotic equivalent relationships for the finite-time ruin probability, respectively. When the distribution of the insurance risk belongs to the dominated varying-tailed distribution class, we obtain asymptotic upper bound and lower bound for the finite-time ruin probability, where for the asymptotic upper bound, we completely get rid of the restriction of mutual independence on insurance risks, and for the lower bound, we only need the insurance risks to have a weak positive association structure. The obtained results extend and improve some existing results.

关键词： finite-time ruin probability dominated varying tail insurance risk financial risk

The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks

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Applied Mathematics(A Journal of Chinese Universities) 2014年第2期29卷 194-204页

作者： YANG Yang LIN Jin-guan TAN Zhong-quan School of Mathematics and Statistics Nanjing Audit University School of Economics and Management Southeast University Department of Mathematics Southeast University College of Mathematics Physics and Information Engineering Jiaxing University

Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {（Xi, Yi）, i≥1） form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.

关键词： Asymptotics long-tailed and dominatedly-varying-tailed distribution financial and insurancerisks finite-time ruin probability bivariate Sarmanov distribution.

Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate

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Journal of Southeast University(English Edition) 2014年第1期30卷 118-121页

作者：杨洋刘伟林金官张玉林东南大学经济管理学院南京210096 南京审计学院数学与统计学院南京210029 新疆大学数学与系统科学学院乌鲁木齐830046 东南大学数学系南京210096

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.

关键词： compound and non-compound risk models finite-time ruin probability dominatedly varying tail uniformasymptotics random sums dependence structure

Asymptotic for the finite-time ruin probability in the Renewal Risk Model with Constantinterest Force

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Asymptotic for the Finite-Time Ruin Probability in the Renew...

Uniform Asymptotics for finite-time ruin Probabilities of Risk Models with Non-Stationary Arrivals and Strongly Subexponential Claim Sizes

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作者： Hai-zhong Yang,Jing Wei School of Statistics,Xi’an University of Finance and Economics,Xi’an 710100,China

Chen and Ng investigated the infinite time ruin probability of the renewal risk model with constant interest and extended regularly varying tailed *** the techniques developed by Chen and Ng,the note derives a simple ... 详细信息

关键词： Asymptotics finite-time ruin probability the renewal risk model

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Wuhan University Journal of Natural Sciences 2024年第1期29卷 21-28页

作者： XU Chenghao WANG Kaiyong PENG Jiangyan School of Mathematical Sciences Suzhou University of Science and TechnologySuzhou 215009JiangsuChina School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu 611731SichuanChina

This paper considers the one-and two-dimensional risk models with a non-stationary claim-number *** the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim ***,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.

关键词： one-dimensional risk model two-dimensional risk model large deviations principle finite-time ruin probability heavy-tailed distributions

Large-deviation probabilities for maxima of sums of subexponential random variables with application to finite-time ruin probabilities

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Science China Mathematics 2008年第7期51卷 1257-1265页

作者： JIANG Tao School of Finance,Zhejiang Gongshang University,Hangzhou 310018,China School of Finance Zhejiang Gongshang University Hangzhou China

We establish an asymptotic relation for the large-deviation probabilities of the maxima of sums of subexponential random variables centered by multiples of order statistics of *** uniform random *** extends a corresponding result of *** an application,we generalize a result of Tang,the uniform asymptotic estimate for the finite-time ruin probability,to the whole strongly subexponential class.

关键词： large-deviation probability strongly subexponential distribution finite-time ruin probability the compound Poisson model uniform asymptotics 91B30 60G70 62P05