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Ruin probability in a two-dimensional model with correlated Brownian motions

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  • Peter Grandits
  • Maike Klein

Abstract

We consider two insurance companies with endowment processes given by Brownian motions with drift. The firms can collaborate by transfer payments in order to maximize the probability that none of them goes bankrupt. We show that pushing maximally the company with less endowment is the optimal strategy for the collaboration if the Brownian motions are correlated and the transfer rate can exceed the drift rates. Moreover, we obtain an explicit formula for the minimal ruin probability in case of perfectly positively correlated Brownian motions where we also allow for different diffusion coefficients.

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  • Peter Grandits & Maike Klein, 2020. "Ruin probability in a two-dimensional model with correlated Brownian motions," Papers 2004.13601, arXiv.org.
    • Handle: RePEc:arx:papers:2004.13601
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    References listed on IDEAS

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    1. Hans Gerber & Elias Shiu, 2006. "On The Merger Of Two Companies," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(3), pages 60-67.
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    4. Avram, Florin & Palmowski, Zbigniew & Pistorius, Martijn, 2008. "A two-dimensional ruin problem on the positive quadrant," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 227-234, February.
    5. Jia-Wen Gu & Mogens Steffensen & Harry Zheng, 2018. "Optimal Dividend Strategies of Two Collaborating Businesses in the Diffusion Approximation Model," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 377-398, May.
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