Upper bounds for ruin probabilities under model uncertainty

2018 ◽  
Vol 48 (18) ◽  
pp. 4511-4527 ◽  
Author(s):  
Zhongyang Sun
Keyword(s):  
Model Uncertainty ◽  
Upper Bounds ◽  
Ruin Probabilities

scholarly journals Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes

2001 ◽  
Vol 31 (1) ◽  
pp. 59-79 ◽  
Author(s):  
M. Usábel
Keyword(s):  
Laplace Transform ◽  
Laplace Transforms ◽  
Upper Bounds ◽  
Interesting Property ◽  
Ruin Probabilities ◽  
Lower And Upper Bounds ◽  
Recursive Methods ◽  
Stable Algorithm ◽  
The Laplace Transform ◽  
Generalized Gamma Convolutions

AbstractA method of inverting the Laplace transform based on the integration between zeros technique and a simple acceleration algorithm is presented. This approach was designed to approximate ultimate ruin probabilities for Γ-convolutions claim sizes, but it can be also used with other distributions. The stable algorithm obtained yields interval approximations (lower and upper bounds) to any desired degree of accuracy even for very large values of u (1,000,000), initial reserves, without increasing the number of computations. This last fact can be considered an interesting property compared with other recursive methods previously used in actuarial literature or other methods of inverting Laplace transforms.

DISCRETE TIME RISK MODELS UNDER RATES OF INTEREST

2002 ◽  
Vol 16 (3) ◽  
pp. 309-324 ◽  
Author(s):  
Jun Cai
Keyword(s):  
Discrete Time ◽  
Upper Bounds ◽  
Ruin Probabilities ◽  
Risk Models ◽  
Recursive Techniques

Two discrete time risk models under rates of interest are introduced. Ruin probabilities in the two risk models are discussed. Stochastic inequalities for the ruin probabilities are derived by martingales and renewal recursive techniques. The inequalities can be used to evaluate the ruin probabilities as upper bounds. Numerical illustrations for these results are given.

Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains

2014 ◽  
Vol 4 (3) ◽  
pp. 283-300
Author(s):  
Phung Duy Quang
Keyword(s):  
Markov Chain ◽  
Ruin Probability ◽  
Risk Process ◽  
Upper Bounds ◽  
Ruin Probabilities ◽  
Countable Number ◽  
Probability Inequalities ◽  
Homogenous Markov Chain ◽  
Recursive Equations ◽  
Risk Processes

AbstractThis article explores recursive and integral equations for ruin probabilities of generalised risk processes, under rates of interest with homogenous Markov chain claims and homogenous Markov chain premiums. We assume that claim and premium take a countable number of non-negative values. Generalised Lundberg inequalities for the ruin probabilities of these processes are derived via a recursive technique. Recursive equations for finite time ruin probabilities and an integral equation for the ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.

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