Titlebook: Lundberg Approximations for Compound Distributions with Insurance Applications; Gordon E. Willmot,X. Sheldon Lin Book 2001 Springer Scienc

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Mixed Poisson distributions,tion is often used to model the number of losses or claims arising from a group of risks where the risk level among the group retains heterogeneity which can not be classified by underwriting criteria. However, it may be reasonable to assume that the risk level follows a probability distribution, an

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Compound distributions,d distribution represents the number of claims arising from the insurance portfolio while the associated sequence of iid random variables represents consecutive individual claim amounts. Various quantities of interest such as stop-loss premiums and risk premiums which arise in insurance are closely

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Bounds based on reliability classifications,Simpler bounds are thus derived in the corollaries of these theorems and they are applicable for an arbitrary individual claim amount df .(.). In this chapter we employ the results of chapter 4 with additional assumptions about the df .(.). By taking advantage of reliability properties of .(.), refi

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Parametric Bounds,xponential bounds. An exponential bound on the tail probability is often considered for a distribution whose moment generating function exists. In this case, a simple exponential upper bound can be obtained by applying Markov’s inequality but it is often unsatisfactory, as was demonstrated in sectio

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Tijms approximations,chapters, we have discussed upper and lower bounds on compound distribution tails. In this chapter various approximations are considered. These approximations are motivated by an approximation given in Tijms (1986, p. 61), in which Tijms proposed the use of a combination of two exponentials to appro

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Defective renewal equations,n in many queueing models and the number of offspring distribution in branching processes satisfy certain defective renewal equations. For a detailed discussion of these applications, see Feller (1971) or Resnick (1992). Defective renewal equations also play an important role in insurance risk theor

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The severity of ruin,y be viewed as an expected discounted penalty introduced in section 9.2, where the penalty function .(.) takes a special form. As discussed in section 9.2, we are thus able to express the conditional distribution of the deficit as the solution of a defective renewal equation, which conveniently lead

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