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Pricing Of Unemployment Insurance Products With Doubly Stochastic Markov Chains

  • FRANCESCA BIAGINI

    ()

    (Department of Mathematics, Group of Financial Mathematics and Stochastics, University of Munich (LMU), Theresienstraße 39, 80333 Munich, Germany)

  • JAN WIDENMANN

    ()

    (Department of Mathematics, Group of Financial Mathematics and Stochastics, University of Munich (LMU), Theresienstraße 39, 80333 Munich, Germany)

Registered author(s):

    This paper provides a new approach for modeling and calculating premiums for unemployment insurance products. The innovative modeling concept consists of combining the benchmark approach with its real-world pricing formula and Markov chain techniques in a doubly stochastic setting. We describe individual insurance claims based on a special type of unemployment insurance contracts, which are offered on the private insurance market. The pricing formulas are first given in a general setting and then specified under the assumption that the individual employment-unemployment process of an employee follows a time-homogeneous doubly stochastic Markov chain. In this framework, formulas for the premiums are provided depending on the ℙ-numéraire portfolio of the benchmark approach. Under a simple assumption on the ℙ-numéraire portfolio, the model is tested on its sensitivities to several parameters. With the same specification the model's employment and unemployment intensities are estimated on public data of the Federal Employment Office in Germany.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 15 (2012)
    Issue (Month): 04 ()
    Pages: 1250025-1-1250025-32

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    Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:04:p:1250025-1-1250025-32
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    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
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    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    7. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Papers 1210.2337, arXiv.org.
    8. Sondermann, Dieter, 1991. "Reinsurance in arbitrage-free markets," Insurance: Mathematics and Economics, Elsevier, vol. 10(3), pages 191-202, December.
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    10. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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