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.
Insurance, Modelling, Net worth, Transfer processes
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