# Accession Number:

## ADA012984

# Title:

## Risk Processes with Compounding Assets.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH

# Personal Author(s):

# Report Date:

## 1975-01-22

# Pagination or Media Count:

## 45.0

# Abstract:

The paper considers a generalization of the classical model of collective risk theory. It is assumed that the cumulative income of a firm is given by a stochastic process Xt with stationary, independent increments, and that interest is earned continuously on the firms cash assets. It is shown that Yt, the assets of the firm at time t, can be expressed as a simple path-wise integral with respect to the income process X.. The behavior of the assets process is studied, much of the analysis focusing on the probability ry that assets will ever fall to zero when the initial asset level is y. The author calls r. the ruin function. A variety of general results are proved, culminating in a useful characterization of the ruin function. From this the author obtains a general upper bound for ry and a general solution for ry in the case where X. has no negative jumps. The ruin function is explicitly calculated for three particular examples. In addition, an approximation theorem is proved using the formal machinery of the weak convergence theory for stochastic processes.

# Subject Categories:

- Economics and Cost Analysis
- Operations Research