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

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.