Moderate- and Large- Deviation Probabilities in Actuarial Risk Theory,

Abstract

A general model for the actuarial Risk Reserve Process as a superposition of compound delayed-renewal processes is introduced and related to previous models which have been used in Collective Risk Theory. it is observed that nonstationarity of the portfolio age-structure within this model can have a significant impact upon probabilities of ruin. When the portfolio size is constant and the policy age-distribution is stationary, the moderate- and large- deviation probabilities of ruin are bounded and calculated using the strong approximation results of Csorgo, Horvath and Steinebach (1987) and a large-deviation theorem of Groeneboom, Oosterhoff, and Ruymgaart (1979). One consequence is that for non-Poisson claim-arrivals, the large-deviation probabilities of ruin are noticeably affected by the decision to model many parallel policy lines in place of one line with correspondingly faster claim-arrivals. Keywords: Asymptotics; Mathematical models. (KR)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1988
Accession Number
ADA195820

Entities

People

  • Craig Hoesman
  • Eric V. Slud

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Age Distribution
  • Analytic Functions
  • Markov Processes
  • Mathematical Models
  • Mathematics
  • Military Research
  • Models
  • Probability
  • Random Variables
  • Security
  • Sequences
  • Stationary
  • Stationary Processes
  • Statistics
  • Stochastic Processes
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Astronomy/Astrophysics
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms