Accession Number:

AD0678413

Title:

DIFFUSION APPROXIMATIONS IN COLLECTIVE RISK THEORY.

Descriptive Note:

Technical rept.,

Corporate Author:

STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH

Personal Author(s):

Report Date:

1968-07-08

Pagination or Media Count:

17.0

Abstract:

Collective risk theory is concerned with the random fluctuations of the total assets of an insurance company. The company has an initial capital u and policyholders pay a gross risk premium of a per unit time. At the jumps of a renewal process claims are made against the company for random amounts with the average claim being mu. A sequence of risk reserve processes which measure the companies assets at time t are defined and the theory of weak convergence of probability measures on function spaces is applied to show that the sequence converges weakly to a limiting diffusion process. This diffusion is Brownian motion with a drift. Weak convergence theory also yields a limit theorem for the distribution of time to ruin. The density for this limit distribution is given explicitly. Author

Subject Categories:

  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE