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) : Iglehart,Donald L.

Report Date : 08 JUL 1968

Pagination or Media Count : 17

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)

Descriptors :   (*PROBABILITY, MONEY), STATISTICAL PROCESSES, MEASURE THEORY, APPROXIMATION(MATHEMATICS), SEQUENCES(MATHEMATICS), CONVERGENCE, DIFFUSION, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE