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Risks 2016, 4(4), 42; doi:10.3390/risks4040042

Optimal Premium as a Function of the Deductible: Customer Analysis and Portfolio Characteristics

Department of Mathematics, Aarhus University, 8000 Aarhus C, Denmark
Academic Editor: Qihe Tang
Received: 1 September 2016 / Revised: 17 October 2016 / Accepted: 3 November 2016 / Published: 9 November 2016
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Abstract

An insurance company offers an insurance contract ( p , K ) , consisting of a premium p and a deductible K. In this paper, we consider the problem of choosing the premium optimally as a function of the deductible. The insurance company is facing a market of N customers, each characterized by their personal claim frequency, α, and risk aversion, β. When a customer is offered an insurance contract, she/he will, based on these characteristics, choose whether or not to insure. The decision process of the customer is analyzed in detail. Since the customer characteristics are unknown to the company, it models them as i.i.d. random variables; A 1 , , A N for the claim frequencies and B 1 , , B N for the risk aversions. Depending on the distributions of A i and B i , expressions for the portfolio size n ( p ; K ) [ 0 , N ] and average claim frequency α ( p ; K ) in the portfolio are obtained. Knowing these, the company can choose the premium optimally, mainly by minimizing the ruin probability. View Full-Text
Keywords: microeconomic insurance; customer characteristics; portfolio size; average claim frequency; ruin theory microeconomic insurance; customer characteristics; portfolio size; average claim frequency; ruin theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Thøgersen, J. Optimal Premium as a Function of the Deductible: Customer Analysis and Portfolio Characteristics. Risks 2016, 4, 42.

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