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Optimal streams of premiums in multiperiod credibility models
L. Gajek1 ; P. Mi/s2 ; J. S/lowi/nska3
1 Institute of Mathematics Technical University of /L/od/x W/olcza/nska 215 90-924 /L/od/x, Poland and Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Technical University of /L/od/x W/olcza/nska 215 90-924 /L/od/x, Poland
3 Computer System Section Department of Computer Science Faculty of Science Vrije Universiteit De Boelelaan 1081 1081 HV Amsterdam, The Netherlands
Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 223-235 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) “anticipating premiums”. It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period credibility premiums.
DOI : 10.4064/am34-2-7
Keywords: optimal arrangement stream insurance premiums multiperiod insurance policy considered order satisfy solvency requirements assume weak axiom solvency satisfied optimization problems solved finding stream net premiums approximates optimally future claims anticipating premiums shown resulting optimal streams premiums enable differentiating between policyholders much quickly one period credibility premiums

L. Gajek 1 ; P. Mi/s 2 ; J. S/lowi/nska 3

1 Institute of Mathematics Technical University of /L/od/x W/olcza/nska 215 90-924 /L/od/x, Poland and Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Technical University of /L/od/x W/olcza/nska 215 90-924 /L/od/x, Poland
3 Computer System Section Department of Computer Science Faculty of Science Vrije Universiteit De Boelelaan 1081 1081 HV Amsterdam, The Netherlands 
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     title = {Optimal streams of premiums in multiperiod
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     journal = {Applicationes Mathematicae},
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L. Gajek; P. Mi/s; J. S/lowi/nska. Optimal streams of premiums in multiperiod
 credibility models. Applicationes Mathematicae, Tome 34 (2007) no. 2, pp. 223-235. doi: 10.4064/am34-2-7

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