Nonparametric Estimation of the Probability of Ruin.

Abstract

The finite and infinite horizon time probability of ruin are important parameters in the study of acturial risk theory. This paper introduces procedures for directly estimating these key parameters from a random sample of observations without assumptions as to the parametric form of the distribution from which the observations arise. The estimators introduced apply to most of the classical models in which ruin probabilities are used and also apply to a much broader class of models. The procedures are based on the concept of sample reuse, and old idea in statistics which is becoming more popular due to the widespread availability of high speed computers. In this paper, the almost sure consistency of the estimators is established, Further, finite sample properties of the estimators are investigated in a simulation study. Keywords: Reverse martingdale, Bootstrap.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1985
Accession Number
ADA153523

Entities

People

  • E. W. Frees

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computations
  • Computers
  • Consistency
  • Data Science
  • Distribution Functions
  • Human Behavior
  • Information Science
  • Mathematics
  • Monte Carlo Method
  • Permutations
  • Probability
  • Random Variables
  • Simulations
  • Statistical Samples
  • Statistics
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Software Engineering.
  • Statistical inference.