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

Jiandong Ren

Journal of Risk Finance, 2005, vol. 6, issue 2, 98-117

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: Transfer processes; Modelling; Insurance; Net worth (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eme:jrfpps:15265940510585789

DOI: 10.1108/15265940510585789

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