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Some Discussion Of Ruin Probability In Risk Models With Processes By Diffusion Under Heavy-tailed Claims

Posted on:2012-03-25Degree:MasterType:Thesis
Country:ChinaCandidate:N N WangFull Text:PDF
GTID:2309330467978928Subject:Probability theory and mathematical statistics
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This thesis is devoted to the development of ruin theory in different risk models. The main research of the basic model is the classical risk model and delay renewal risk model, and chapters in this paper are carried through based upon the heavy-tailed distributions. Considering that most financial researchers have not considered stochastic diffusion in the studies of risk theory. This thesis add risk process perturbed by diffusion to the model considering insurance companies have indefinite income and payout.It is organized as follows:This thesis firstly introduced ruin probability and some commonly used heavy-tailed subfamily; subexponential distributions as a kind class of heavy-tailed distributions. And then discussed some important properties of subexponential distribution and heavy-tailed distribution.Secondly, random disturbance classical risk model was defined. In the classical risk process that is perturbed by diffusion., if the equilibrium distribution function Fe∈S,then ruin probability Ψ(x)~ρ-1Fe(x).Thirdly, two risk models were introduced:delayed renewal risk model and generalized delay renewal risk model. This thesis prove in the delay renewal risk model with the safety loading condition ρ>0,if distribution function F∈D, then the tail equivalence relationship holds.Lastly, the generalized classical risk process by diffusion was defined. Introduce the concept of adjustment coefficient, discuss the character of surplus process, and get Lundberg inequality and formula of the ruin probability using two methods of traditional method and martingale.
Keywords/Search Tags:diffusion, ruin probability, heavy-tailed distribution, subexponential distributionclassical risk model
PDF Full Text Request
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