DIFFUSION APPROXIMATIONS IN COLLECTIVE RISK THEORY.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 08, 1968
- Accession Number
- AD0678413
Entities
People
- Donald Iglehart
Organizations
- Stanford University