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