scholarly journals Upper bounds for ruin probabilities in a new general risk model, by the martingales method

1982 ◽  
Vol 8 (2) ◽  
pp. 121-126
Author(s):  
F. De Vylder ◽  
M.J. Goovaerts
Keyword(s):  
Risk Model ◽  
Upper Bounds ◽  
Ruin Probabilities

scholarly journals UPPER BOUNDS FOR RUIN PROBABILITY UNDER TIME SERIES MODELS

2006 ◽  
Vol 20 (3) ◽  
pp. 529-542 ◽  
Author(s):  
Gary K. C. Chan ◽  
Hailiang Yang
Keyword(s):  
Time Series ◽  
Ruin Probability ◽  
Causal Model ◽  
Risk Model ◽  
Upper Bounds ◽  
Time Series Models ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Special Cases ◽  
Insurance Risk Model

In this article, we consider an insurance risk model where the claim and premium processes follow some time series models. We first consider the model proposed in Gerber [2,3]; then a model with dependent structure between premium and claim processes modeled by using Granger's causal model is considered. By using some martingale arguments, Lundberg-type upper bounds for the ruin probabilities under both models are obtained. Some special cases are discussed.

Ruin probabilities for a risk model with two classes of claims

2010 ◽  
Vol 26 (9) ◽  
pp. 1749-1760 ◽  
Author(s):  
Tong Ling Lv ◽  
Jun Yi Guo ◽  
Xin Zhang
Keyword(s):  
Risk Model ◽  
Ruin Probabilities

Asymptotic ruin probabilities for a bidimensional renewal risk model

Stochastics ◽  
2017 ◽  
Vol 89 (5) ◽  
pp. 687-708 ◽  
Author(s):  
Haizhong Yang ◽  
Jinzhu Li
Keyword(s):  
Risk Model ◽  
Ruin Probabilities ◽  
Renewal Risk Model ◽  
Renewal Risk

scholarly journals On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

1984 ◽  
Vol 14 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Jean-Marie Reinhard
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Risk Models ◽  
Markovian Environment ◽  
Necessary And Sufficient ◽  
Natural Way ◽  
Quantities Of Interest

AbstractWe consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

scholarly journals Ruin Probabilities in a Finite-Horizon Risk Model with Investment and Reinsurance

2012 ◽  
Vol 49 (04) ◽  
pp. 954-966
Author(s):  
R. Romera ◽  
W. Runggaldier
Keyword(s):  
Financial Market ◽  
Continuous Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Horizon ◽  
Ruin Probabilities ◽  
Optimal Solutions ◽  
Semi Markov Process ◽  
Insurance Model ◽  
Recursive Relations

A finite-horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Our setting is innovative in the sense that we describe in a unified way the timing of the events, that is, the arrivals of claims and the changes of the prices in the financial market, by means of a continuous-time semi-Markov process which appears to be more realistic than, say, classical diffusion-based models. Obtaining explicit optimal solutions for the minimizing ruin probability is a difficult task. Therefore we derive a specific methodology, based on recursive relations for the ruin probability, to obtain a reinsurance and investment policy that minimizes an exponential bound (Lundberg-type bound) on the ruin probability.

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