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
An insurance company offers an insurance contract
, 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;
for the claim frequencies and
for the risk aversions. Depending on the distributions of
, expressions for the portfolio size
and average claim frequency
in the portfolio are obtained. Knowing these, the company can choose the premium optimally, mainly by minimizing the ruin probability.
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.
Thøgersen J. Optimal Premium as a Function of the Deductible: Customer Analysis and Portfolio Characteristics. Risks. 2016; 4(4):42.
Thøgersen, Julie. 2016. "Optimal Premium as a Function of the Deductible: Customer Analysis and Portfolio Characteristics." Risks 4, no. 4: 42.
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