scholarly journals Infinite time ruin probability in inhomogeneous claims case

2010 ◽  
Vol 51 ◽  
Author(s):  
Eugenija Bieliauskienė ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Recursive Formula ◽  
Infinite Time

The article deals with the classical discrete-time risk model with non-identically distributed claims. The recursive formula of infinite time ruin probability is obtained, which enables to evaluate the probability to ruin with desired accuracy.

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

scholarly journals MARTINGALE METHOD FOR RUIN PROBABILITY IN AN AUTOREGRESSIVE MODEL WITH CONSTANT INTEREST RATE

2003 ◽  
Vol 17 (2) ◽  
pp. 183-198 ◽  
Author(s):  
Hailiang Yang ◽  
Lihong Zhang
Keyword(s):  
Interest Rate ◽  
Autoregressive Model ◽  
Ruin Probability ◽  
Risk Model ◽  
Martingale Method ◽  
Insurance Risk ◽  
Infinite Time ◽  
Probability Of Ruin ◽  
Constant Interest Rate ◽  
Constant Interest

In this article, we consider a discrete-time insurance risk model. An autoregressive model is used to model both the claim process and the premium process. The probability of ruin is examined in a model with a constant interest rate. Both exponential and nonexponential upper bounds are obtained for the ruin probability of an infinite time horizon.

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.

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