scholarly journals Precise large deviation of claim surplus process in a risk model with variable premium and NA claims

2017 ◽  
Author(s):  
Yinghua Dong
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Surplus Process ◽  
Precise Large Deviation

Precise Large Deviation of Claim Surplus Process in a Renewal Risk Model with Random Premium Income

2013 ◽  
Vol 850-851 ◽  
pp. 771-775
Author(s):  
Ying Hua Dong
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Compound Poisson Process ◽  
Dependence Structure ◽  
Arrival Times ◽  
Renewal Risk Model ◽  
Surplus Process ◽  
Precise Large Deviation ◽  
Renewal Risk ◽  
Premium Income

In this paper, we consider a nonstandard renewal risk model in which claim sizes and corresponding inter-arrival times form a sequence of independent and identically distributed random pairs. Each pair satisfies a certain dependence structure. In addition, premium income is described by a compound Poisson process. When the distribution of claim sizes belongs to the consistent variation class, we obtain precise large deviation of claim surplus process.

Precise Large Deviation of Claim Surplus Process in a Risk Model with END Claim Sizes

2014 ◽  
Vol 687-691 ◽  
pp. 4482-4484
Author(s):  
Ying Hua Dong
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Random Variables ◽  
Renewal Processes ◽  
Dependent Random Variables ◽  
Insurance Policies ◽  
Surplus Process ◽  
Negatively Dependent Random Variables ◽  
Precise Large Deviation

In this paper, we study a risk model in which the claim sizes are extended negatively dependent random variables with consistently varying tails, and the arrival of the successive insurance policies forms a nonstandard renewal processes. For this risk model, we give the precise large deviation of the claim surplus process.

Precise large deviations for the prospective-loss process

2003 ◽  
Vol 40 (02) ◽  
pp. 391-400 ◽  
Author(s):  
Kai W. Ng ◽  
Qihe Tang ◽  
Jiaan Yan ◽  
Hailiang Yang
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Arrival Process ◽  
Insurance Risk ◽  
Precise Large Deviations ◽  
Loss Process ◽  
Mild Assumption ◽  
Random Index ◽  
Precise Large Deviation ◽  
Heavy Tailed

In this paper, we propose a customer-arrival-based insurance risk model, in which customers' potential claims are described as independent and identically distributed heavy-tailed random variables and premiums are the same for each policy. We obtain some precise large deviation results for the prospective-loss process under a mild assumption on the random index (in our case, the customer-arrival process), which is much weaker than that in the literature.

Precise large deviations for the prospective-loss process

2003 ◽  
Vol 40 (2) ◽  
pp. 391-400 ◽  
Author(s):  
Kai W. Ng ◽  
Qihe Tang ◽  
Jiaan Yan ◽  
Hailiang Yang
Keyword(s):  
Risk Model ◽  
Large Deviation ◽  
Arrival Process ◽  
Insurance Risk ◽  
Precise Large Deviations ◽  
Loss Process ◽  
Mild Assumption ◽  
Random Index ◽  
Precise Large Deviation ◽  
Heavy Tailed

In this paper, we propose a customer-arrival-based insurance risk model, in which customers' potential claims are described as independent and identically distributed heavy-tailed random variables and premiums are the same for each policy. We obtain some precise large deviation results for the prospective-loss process under a mild assumption on the random index (in our case, the customer-arrival process), which is much weaker than that in the literature.

scholarly journals ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

2014 ◽  
Vol 44 (3) ◽  
pp. 635-651 ◽  
Author(s):  
Chuancun Yin ◽  
Yuzhen Wen ◽  
Yongxia Zhao
Keyword(s):  
Lévy Process ◽  
Risk Model ◽  
Levy Process ◽  
Dual Model ◽  
Threshold Strategy ◽  
Classical Risk Model ◽  
Surplus Process ◽  
Optimal Dividend ◽  
Special Cases ◽  
The Classical Risk Model

AbstractIn this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

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