PRICING OF UNEMPLOYMENT INSURANCE PRODUCTS WITH DOUBLY STOCHASTIC MARKOV CHAINS

Francesca Biagini () and Jan Widenmann ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2012, vol. 15, issue 04, 1-32

Abstract: 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.

Keywords: Unemployment insurance; benchmark approach; doubly stochastic Markov chain; actuarial martingale pricing; intensity based approach (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024912500252

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