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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.

Suggested Citation

  • Peter Grandits & Maike Klein, 2021. "Ruin probability in a two-dimensional model with correlated Brownian motions," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(5), pages 362-379, May.
    • Handle: RePEc:taf:sactxx:v:2021:y:2021:i:5:p:362-379
    DOI: 10.1080/03461238.2020.1845788
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