Two Papers on Recursive Evaluation of Compound Distributions.

Abstract

(Title: Further Results on Recursive Evaluation of Compound Distributions.)(Abstract:) A recent result by Panjer provides a recursive algorithm for the compound distribution of aggregate claims when the counting law belongs to a special recursive family. In the present paper we first give a characterization of this recursive family, then describe some generalizations of Panjer's result. (Title: Improved Approximations for the Distribution of a Heterogeneous Risk Portfolio). (Abstract:) A traditional actuarial method for the difficult task of finding the exact distribution of a heterogeneous portfolio approximates the distribution with a compound Poisson law with identically distributed risks. This paper shows that a Binomial compound law provides a better match to the second moment of the distribution, thus giving a better approximation, while retaining a simple, recursive algorithm for calculating the distribution. A modified Binomial compound law further refines the approximation, with slight additional work.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1981
Accession Number
ADA107912

Entities

People

  • Bjorn Sundt
  • Willian S. Jewell

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Binomials
  • California
  • Computations
  • Convolution
  • Digital Computers
  • Discrete Distribution
  • Mathematics
  • Operations Research
  • Probability
  • Random Variables
  • Scientific Research
  • Sequences
  • Test And Evaluation
  • United States
  • Universities

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.