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Portfolio size as function of the premium: modelling and optimization

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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.

Original languageEnglish
JournalStochastics: An International Journal of Probability and Stochastic Processes
Volume85
Issue4 (Taksar Memorial Issue)
Pages (from-to)575-588
Number of pages14
ISSN1744-2508
DOIs
Publication statusPublished - 2013

    Research areas

  • adverse selection, certainty equivalent, Cramér-Lundberg model, diffusion approximation, inverse Gamma distribution, Lambert W function

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