scholarly journals Ruin Probabilities in a Dependent Discrete-Time Risk Model With Gamma-Like Tailed Insurance Risks

Risks ◽  
2017 ◽  
Vol 5 (1) ◽  
pp. 14 ◽  
Author(s):  
Xing-Fang Huang ◽  
Ting Zhang ◽  
Yang Yang ◽  
Tao Jiang
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Ruin Probabilities

scholarly journals Ruin Probabilities of a Discrete-time Multi-risk Model

2015 ◽  
Vol 44 (4) ◽  
pp. 367-379 ◽  
Author(s):  
Andrius Grigutis ◽  
Agneška Korvel ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Arrival Time ◽  
Risk Model ◽  
Recursive Formula ◽  
Ruin Probabilities ◽  
Numerical Examples ◽  
Premium Rate ◽  
Insurance Business ◽  
Independent Series

In this work,  we investigate a  multi-risk model describing insurance business with  two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed   inter-arrival time. Claim amounts occur until they   can be compensated by a common premium rate and the initial insurer's surplus.  In this article, wederive a recursive formula for calculation of finite-time ruin probabilities. In the case of bi-risk model, we present a procedure to calculate the ultimate ruin probability. We add several numerical examples illustrating application  of the derived formulas.DOI: http://dx.doi.org/10.5755/j01.itc.44.4.8635

ASYMPTOTIC RUIN PROBABILITIES IN FINITE HORIZON WITH SUBEXPONENTIAL LOSSES AND ASSOCIATED DISCOUNT FACTORS

2005 ◽  
Vol 20 (1) ◽  
pp. 103-113 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Stochastic Processes ◽  
Discrete Time ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Finite Time Ruin Probability ◽  
Discount Factors ◽  
Subexponential Class

Consider a discrete-time insurance risk model with risky investments. Under the assumption that the loss distribution belongs to a certain subclass of the subexponential class, Tang and Tsitsiashvili (Stochastic Processes and Their Applications 108(2): 299–325 (2003)) established a precise estimate for the finite time ruin probability. This article extends the result both to the whole subexponential class and to a nonstandard case with associated discount factors.

scholarly journals Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment

Risks ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 26
Author(s):  
Dhiti Osatakul ◽  
Xueyuan Wu
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Insurance Industry ◽  
External Environment ◽  
Ruin Probabilities ◽  
Risk Models ◽  
Markovian Environment ◽  
Life Insurance Industry ◽  
Claim Frequency ◽  
The Impact

In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability.

scholarly journals On a discrete-time risk model with claim correlated premiums

2015 ◽  
Vol 9 (2) ◽  
pp. 322-342 ◽  
Author(s):  
Xueyuan Wu ◽  
Mi Chen ◽  
Junyi Guo ◽  
Can Jin
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Insurance Industry ◽  
Joint Probability ◽  
Ruin Probabilities ◽  
Deficit At Ruin ◽  
Probability Of Ruin ◽  
Numerical Examples ◽  
Car Insurance ◽  
The Impact

AbstractThis paper proposes a discrete-time risk model that has a certain type of correlation between premiums and claim amounts. It is motivated by the well-known bonus-malus system (also known as the no claims discount) in the car insurance industry. Such a system penalises policyholders at fault in accidents by surcharges, and rewards claim-free years by discounts. For simplicity, only up to three levels of premium are considered in this paper and recursive formulae are derived to calculate the ultimate ruin probabilities. Explicit expressions of ruin probabilities are obtained in a simplified case. The impact of the proposed correlation between premiums and claims on ruin probabilities is examined through numerical examples. In the end, the joint probability of ruin and deficit at ruin is also considered.

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