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Diffusion models of insurer net worth: can one dimension suffice?

Jiandong Ren (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Canada)

Journal of Risk Finance

ISSN: 1526-5943

Article publication date: 1 April 2005

352

Abstract

Purpose

The paper aims to develop a realistic, yet flexible model of insurer net worth.

Design/methodology/approach

Inspired by and as an improvement to Powers, the paper develops a multi‐dimensional diffusion model to describe the operations of an insurance company. The paper then explores whether or not this multi‐dimensional model can be approximated conservatively by a homogeneous one‐dimensional diffusion.

Findings

The multi‐dimensional model that is proposed can be approximated conservatively by a homogeneous one‐dimensional diffusion, which is clearly much easier to solve analytically or numerically than a multi‐dimensional system. Also, the Laplace transform of the desired first‐passage time (to ruin) distribution can be stated analytically.

Practical implications

The analysis provides a theoretical model of the relationship between the insurer's ruin‐time distribution and many aspects of the insurer's operations, including loss‐payout patterns, premium‐earning patterns, and investment strategy.

Originality/value

The paper reveals that a multi‐dimensional model can be approximated by a homogeneous one‐dimensional diffusion to achieve a realistic and flexible model that can be used practically.

Keywords

Citation

Ren, J. (2005), "Diffusion models of insurer net worth: can one dimension suffice?", Journal of Risk Finance, Vol. 6 No. 2, pp. 98-117. https://doi.org/10.1108/15265940510585789

Publisher

:

Emerald Group Publishing Limited

Copyright © 2005, Emerald Group Publishing Limited

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