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Conditional Ruin Probability with a Markov Regime Switching Model

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Book cover Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

Ruin probabilities have been of a major interest in mathematical insurance. The diffusion process is used to the model of risk reserve of an insurance company usually. In this paper, we introduce a Markov chain and extend the Reserve processes to a jump-diffusion model and research the ruin probabilities. By using stochastic calculus techniques and the Martingale method a partial differential equation satisfied by the finite time horizon conditional ruin probability is obtained.

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Author information

Authors and Affiliations

  1. School of Science, Xi’an Polytechnic University, Xian, 710048, China

    Xuanhui Liu & Li-Ai Cui

  2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Fangguo Ren

Authors
  1. Xuanhui Liu
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  2. Li-Ai Cui
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  3. Fangguo Ren
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Liu, X., Cui, LA., Ren, F. (2011). Conditional Ruin Probability with a Markov Regime Switching Model. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_35

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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