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A Risk Model with an Observer in a Markov Environment

Listed author(s):
  • Hansjörg Albrecher


    (Department of Actuarial Science, University of Lausanne, Lausanne CH-1015, Switzerland
    Swiss Finance Institute, University of Lausanne, Lausanne CH-1015, Switzerland)

  • Jevgenijs Ivanovs


    (Department of Actuarial Science, University of Lausanne, Lausanne CH-1015, Switzerland)

Registered author(s):

    We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 1 (2013)
    Issue (Month): 3 (November)
    Pages: 1-14

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    Handle: RePEc:gam:jrisks:v:1:y:2013:i:3:p:148-161:d:30342
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    1. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    2. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
    3. Mandjes, Michel & Ivanovs, Jevgenijs & Kella, Offer & D'Auria, Bernardo, 2010. "First passage of a Markov additive process and generalized Jordan chains," DES - Working Papers. Statistics and Econometrics. WS ws103923, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Ivanovs, Jevgenijs, 2013. "A note on killing with applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 29-34.
    5. Albrecher, Hansjörg & Lautscham, Volkmar, 2013. "From Ruin to Bankruptcy for Compound Poisson Surplus Processes," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 43(02), pages 213-243, May.
    6. Gerber, Hans U. & Lin, X. Sheldon & Yang, Hailiang, 2006. "A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(02), pages 489-503, November.
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