Ruin Risk Model In Random Fuzzy Environments

Ruin theory is one of hot topic in risk theory. Uncertainty in ruin problems is mainly owing to the interarrival time of claim and the amount of claim. The ruin problem in stochastic environments has been thoroughly studied and achieved fruitful results. But in the real ruin problems, there are always other uncertain phenomena, such as fuzzy random phenomenon, or random fuzzy phenomenon. Till now, the research in this area is still in its infancy stage. Therefore, research how to establish the ruin risk model under random fuzzy environments, would be a great value and theoretical significance.The ruin problem in random fuzzy environments is to be first researched. The ruin risk model in random fuzzy environments is established when the inter-arrival time of claim and the amount of claim are characterized as random fuzzy variables. The mean chance of the ultimate ruin is researched. The expressions of the mean chance of the ultimate ruin is obtained if individual claim amount is an exponentially distributed random fuzzy variable. Furthermore, numerical examples are presented to show how to calculate the mean chance of the ultimate rum.For the ruin problem in random fuzzy environments, the ruin risk model in random fuzzy environments is established if the amount of claim is characterized as a mixed exponentially distributed random fuzzy variable. The mean chance of the ultimate ruin is researched. The expressions of the mean chance of the ultimate ruin is obtained if individual claim amount is a mixed exponentially dis-tributed random fuzzy variable. Furthermore, numerical examples are presented to show how to calculate the mean chance of the ultimate ruin.For the risk order in random fuzzy environments, the concepts and some useful properties of the random fuzzy stop-loss order and the nth random fuzzy stop-loss order are given. Based on the all random fuzzy orders mentioned above, how the individual claim affects the mean chance of the ultimate ruin are explored in random fuzzy compound Poisson ruin risk model. Finally, numerical example is given.For the discrete risk order in random fuzzy environments, the concepts and some useful properties of the discrete random fuzzy order, discrete random fuzzy stop-loss order are given. Based on the all random fuzzy orders mentioned above how the individual claim affects the mean chance of the ultimate ruin are explored in random fuzzy compound binomial ruin risk model.