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Intensity-based premium evaluation for unemployment insurance products

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  • Biagini, Francesca
  • Groll, Andreas
  • Widenmann, Jan

Abstract

We present a flexible premium determination method for insurance products, in particular, for unemployment insurance products. The price is determined with the real-world pricing formula and under the assumption that the employment–unemployment progress of an insured person follows an F-doubly stochastic Markov chain. The stochastic intensity processes are estimated for the German labor market, using Cox’s proportional hazards model with time-dependent covariates on a sample of integrated labor market biographies. The estimation procedure is based on a counting process framework with stochastic compensators, which we show to be naturally connected to the class of F-doubly stochastic Markov chains. Based on the statistical analysis, the prices are computed using Monte Carlo simulations.

Suggested Citation

  • Biagini, Francesca & Groll, Andreas & Widenmann, Jan, 2013. "Intensity-based premium evaluation for unemployment insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 302-316.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:1:p:302-316
    DOI: 10.1016/j.insmatheco.2013.06.001
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    References listed on IDEAS

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    1. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Odd O. Aalen & Johan Fosen & Harald Weedon-Fekjær & Ørnulf Borgan & Einar Husebye, 2004. "Dynamic Analysis of Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 60(3), pages 764-773, September.
    3. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    4. Francesca Biagini & Jan Widenmann, 2012. "Pricing Of Unemployment Insurance Products With Doubly Stochastic Markov Chains," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-32.
    5. Simon, Noah & Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2011. "Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i05).
    6. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    7. Ignatieva, Katja & Platen, Eckhard, 2012. "Estimating the diffusion coefficient function for a diversified world stock index," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1333-1349.
    8. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
    9. Jackson, Christopher, 2011. "Multi-State Models for Panel Data: The msm Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i08).
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    Citations

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    Cited by:

    1. Bielecki, Tomasz R. & Jakubowski, Jacek & Niewęgłowski, Mariusz, 2017. "Conditional Markov chains: Properties, construction and structured dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1125-1170.
    2. Francesca Biagini & Andreas Groll & Jan Widenmann, 2016. "Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains," Risks, MDPI, vol. 4(3), pages 1-26, July.
    3. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.

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    More about this item

    Keywords

    Unemployment insurance; Intensity-based model; F-doubly stochastic Markov chain; Cox proportional hazards model; Benchmark approach;
    All these keywords.

    JEL classification:

    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search
    • J65 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment Insurance; Severance Pay; Plant Closings
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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