# 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

# Descriptors:

# Subject Categories:

- Operations Research