FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W71569118> ?p ?o ?g. }

• W71569118 abstract "This thesis consists of a unified study of bounds and asymptotic estimates for renewal equations and compound distributions and gives applications to aggregate claim distributions, stop-loss premium and ruin probabilities with general claim sizes and especially with heavy-tailed distributions. Chapter 1 presents the probability models of compound distributions and renewal equations in insurance risk analysis and gives the summary of the results of this thesis. In Chapter 2, we develop a general method to construct analytical bounds for solutions of renewal equations. Two-sided exponential and linear estimates for the solutions are derived by this method. A generalized Cramer-Lundberg condition is proposed and used to obtain bounds and asymptotic formulae with NWU distributions for the solutions. Chapter 3 discusses tails of a class of compound distributions introduced by Willmot (1994) and gives uniformly sharper bounds, both with the results obtained in Chapter 2 and renewal theory. The technique of stochastic ordering is employed to get simplified bounds for the tails and to correct the errors of the proofs of some previous results. In Chapter 4, we derive two-sided estimates for tails of a class of aggregate claim distributions, and especially give upper and lower bounds for compound negative binomial distributions both with adjustment coefficients and with heavy-tailed distributions. For the latter case, Dickson's (1994) condition plays the same role as the Cramer-Lundberg condition. Chapter 5 is devoted to the aging property of compound geometric distributions and its applications to stop-loss premiums and ruin probabilities. By the aging property, general upper and lower bounds for the stop-loss premium of the class of compound distributions discussed in Chapter 3 are derived, which apply to any claim size distribution. Also, two-sided estimates for the stop-loss premium of negative binomial sums are obtained both under the Cramer-Lundberg condition and under Dickson's condition. General upper and lower bounds for ruin probabilities are also considered in this chapter. Chapter 6 gives a detailed discussion of the asymptotic estimates of tails of convolutions of compound geometric distributions. Asymptotic estimates for these tails are given under light, medium and heavy-tailed distributions, respectively. Applications of these results are given to the ruin probability in the diffusion risk model. Also, two-sided bounds for the ruin probability are derived by a generalized Dickson condition, which applies to any positive claim size distribution. Finally, we give some examples and consider numerical comparisons of bounds with asymptotic estimates." @default.
• W71569118 created "2016-06-24" @default.
• W71569118 creator A5047248078 @default.
• W71569118 date "1998-01-01" @default.
• W71569118 modified "2023-09-27" @default.
• W71569118 title "A unified study of bounds and asymptotic estimates for renewal equations and compound distributions with applications to insurance risk analysis" @default.
• W71569118 hasPublicationYear "1998" @default.
• W71569118 type Work @default.
• W71569118 sameAs 71569118 @default.
• W71569118 citedByCount "0" @default.
• W71569118 crossrefType "dissertation" @default.
• W71569118 hasAuthorship W71569118A5047248078 @default.
• W71569118 hasConcept C105795698 @default.
• W71569118 hasConcept C108710211 @default.
• W71569118 hasConcept C110121322 @default.
• W71569118 hasConcept C134306372 @default.
• W71569118 hasConcept C154945302 @default.
• W71569118 hasConcept C2524010 @default.
• W71569118 hasConcept C2777212361 @default.
• W71569118 hasConcept C2781315470 @default.
• W71569118 hasConcept C28826006 @default.
• W71569118 hasConcept C33923547 @default.
• W71569118 hasConcept C41008148 @default.
• W71569118 hasConceptScore W71569118C105795698 @default.
• W71569118 hasConceptScore W71569118C108710211 @default.
• W71569118 hasConceptScore W71569118C110121322 @default.
• W71569118 hasConceptScore W71569118C134306372 @default.
• W71569118 hasConceptScore W71569118C154945302 @default.
• W71569118 hasConceptScore W71569118C2524010 @default.
• W71569118 hasConceptScore W71569118C2777212361 @default.
• W71569118 hasConceptScore W71569118C2781315470 @default.
• W71569118 hasConceptScore W71569118C28826006 @default.
• W71569118 hasConceptScore W71569118C33923547 @default.
• W71569118 hasConceptScore W71569118C41008148 @default.
• W71569118 hasLocation W715691181 @default.
• W71569118 hasOpenAccess W71569118 @default.
• W71569118 hasPrimaryLocation W715691181 @default.
• W71569118 hasRelatedWork W1494641395 @default.
• W71569118 hasRelatedWork W1971342095 @default.
• W71569118 hasRelatedWork W2020585108 @default.
• W71569118 hasRelatedWork W2023392881 @default.
• W71569118 hasRelatedWork W2055829188 @default.
• W71569118 hasRelatedWork W2081114409 @default.
• W71569118 hasRelatedWork W2085342432 @default.
• W71569118 hasRelatedWork W2093778745 @default.
• W71569118 hasRelatedWork W2298726439 @default.
• W71569118 hasRelatedWork W2376608625 @default.
• W71569118 hasRelatedWork W2389747659 @default.
• W71569118 hasRelatedWork W2513542451 @default.
• W71569118 hasRelatedWork W2609936126 @default.
• W71569118 hasRelatedWork W2618723292 @default.
• W71569118 hasRelatedWork W2795491171 @default.
• W71569118 hasRelatedWork W2895774457 @default.
• W71569118 hasRelatedWork W2901652583 @default.
• W71569118 hasRelatedWork W3016288520 @default.
• W71569118 hasRelatedWork W3124365696 @default.
• W71569118 hasRelatedWork W3276196 @default.
• W71569118 isParatext "false" @default.
• W71569118 isRetracted "false" @default.
• W71569118 magId "71569118" @default.
• W71569118 workType "dissertation" @default.