Bowley Insurance with Expected Utility Maximization of the Policyholders

North American Actuarial Journal, Forthcoming

24 Pages Posted: 13 Apr 2023

See all articles by Tim J. Boonen

Tim J. Boonen

University of Hong Kong

Wenjun Jiang

University of Calgary

Date Written: March 29, 2023


This paper studies the Bowley solution for a sequential game within the expected utility framework. We assume that the policyholders are expected utility maximizers, and there exists a representative policyholder who faces a fixed loss with given probability and no loss otherwise. This policyholder selects the optimal indemnity function in response to the pricing kernel set by the insurer. Knowing the policyholder’s choice of indemnity function, the insurer adjusts the pricing kernel to maximize its expected net profit. This pricing kernel is of our central interest in this paper, and in our setting the pricing kernel can be evaluated via the safety loading factor in an expected value premium principle. For a wide class of utility functions, we show that the optimal safety loading factor increases with respect to both the policyholder’s risk aversion level and the probability of zero loss. We also show that the insurance contract corresponding to the Bowley solution is Pareto dominated in the sense that both parties’ interests can be further improved, which shows the inefficiency of Bowley solution. Some numerical examples are presented to illustrate the main results, and it is shown that both the policyholder and insurer can strictly benefit from the Bowley solution.

Keywords: Bowley insurance, expected net profit, safety loading factor, Pareto optimality

JEL Classification: C71, G22

Suggested Citation

Boonen, Tim J. and Jiang, Wenjun, Bowley Insurance with Expected Utility Maximization of the Policyholders (March 29, 2023). North American Actuarial Journal, Forthcoming, Available at SSRN: or

Tim J. Boonen (Contact Author)

University of Hong Kong ( email )

Pokfulam Road
Hong Kong

Wenjun Jiang

University of Calgary ( email )

612 Campus Place N.W.
University of Calgary
Calgary, Alberta T2N 1N4

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