Portfolio size as function of the premium: modelling and optimization

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Portfolio size as function of the premium : modelling and optimization. / Asmussen, Søren; Christensen, Bent Jesper; Taksar, Michael.

I: Stochastics, Bind 85, Nr. 4, 19.06.2013, s. 575-588.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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@article{4dc784ba87904042a944cdd88318b172,
title = "Portfolio size as function of the premium: modelling and optimization",
abstract = "An insurance company has a large number N of potential customers characterized by i.i.d. r.v.'s A1,...,AN giving the arrival rates of claims. Customers are risk averse, and a customer accepts an offered premium p according to his A-value. The modelling further involves a discount rate d>r of customers, where r is the risk-free interest rate. Based on calculations of the customers' present values of the alternative strategies of insuring and not insuring, the portfolio size is derived, and also the rate of claims from the insured customers is given. Furthermore, the value of p which is optimal for minimizing the ruin probability is derived in a diffusion approximation to the Cram{\'e}r-Lundberg risk process with an added liability rate L of the company. The solution involves the Lambert W function. Similar discussion is given for extensions involving customers having only partial information on their A and stochastic discount rates.",
keywords = "adverse selection, certainty equivalent, Cram{\'e}r-Lundberg model, diffusion approximation, inverse Gamma distribution, Lambert W function",
author = "S{\o}ren Asmussen and Christensen, {Bent Jesper} and Michael Taksar",
year = "2013",
month = "6",
day = "19",
doi = "10.1080/17442508.2013.797426",
language = "English",
volume = "85",
pages = "575--588",
journal = "Stochastics: An International Journal of Probability and Stochastic Processes",
issn = "1744-2508",
publisher = "Taylor & francis",
number = "4",

}

RIS

TY - JOUR

T1 - Portfolio size as function of the premium

T2 - modelling and optimization

AU - Asmussen, Søren

AU - Christensen, Bent Jesper

AU - Taksar, Michael

PY - 2013/6/19

Y1 - 2013/6/19

N2 - An insurance company has a large number N of potential customers characterized by i.i.d. r.v.'s A1,...,AN giving the arrival rates of claims. Customers are risk averse, and a customer accepts an offered premium p according to his A-value. The modelling further involves a discount rate d>r of customers, where r is the risk-free interest rate. Based on calculations of the customers' present values of the alternative strategies of insuring and not insuring, the portfolio size is derived, and also the rate of claims from the insured customers is given. Furthermore, the value of p which is optimal for minimizing the ruin probability is derived in a diffusion approximation to the Cramér-Lundberg risk process with an added liability rate L of the company. The solution involves the Lambert W function. Similar discussion is given for extensions involving customers having only partial information on their A and stochastic discount rates.

AB - An insurance company has a large number N of potential customers characterized by i.i.d. r.v.'s A1,...,AN giving the arrival rates of claims. Customers are risk averse, and a customer accepts an offered premium p according to his A-value. The modelling further involves a discount rate d>r of customers, where r is the risk-free interest rate. Based on calculations of the customers' present values of the alternative strategies of insuring and not insuring, the portfolio size is derived, and also the rate of claims from the insured customers is given. Furthermore, the value of p which is optimal for minimizing the ruin probability is derived in a diffusion approximation to the Cramér-Lundberg risk process with an added liability rate L of the company. The solution involves the Lambert W function. Similar discussion is given for extensions involving customers having only partial information on their A and stochastic discount rates.

KW - adverse selection

KW - certainty equivalent

KW - Cramér-Lundberg model

KW - diffusion approximation

KW - inverse Gamma distribution

KW - Lambert W function

UR - http://www.scopus.com/inward/record.url?scp=84883489081&partnerID=8YFLogxK

U2 - 10.1080/17442508.2013.797426

DO - 10.1080/17442508.2013.797426

M3 - Journal article

VL - 85

SP - 575

EP - 588

JO - Stochastics: An International Journal of Probability and Stochastic Processes

JF - Stochastics: An International Journal of Probability and Stochastic Processes

SN - 1744-2508

IS - 4

ER -