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Simultaneous ruin probability for two-dimensional brownian risk model

Part of: Stochastic processes

Published online by Cambridge University Press:  16 July 2020

Krzysztof Dȩbicki ,
Enkelejd Hashorva  and
Zbigniew Michna
Krzysztof Dȩbicki*
Affiliation:
University of Wrocław
Enkelejd Hashorva*
Affiliation:
University of Lausanne
Zbigniew Michna*
Affiliation:
Wrocław University of Economics and Business
*
*Postal address: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email: Krzysztof.Debicki@math.uni.wroc.pl
**Postal address: Department of Actuarial Science, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland. Email: Enkelejd.Hashorva@unil.ch
***Postal address: Department of Logistics, Wrocław University of Economics and Business, Komandorska 118/120, 53-345 Wrocław, Poland. Email: zbigniew.michna@ue.wroc.pl
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Abstract

The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite time horizon. This is not the case for the simultaneous ruin probability in the two-dimensional Brownian risk model. Relying on asymptotic theory, we derive in this contribution approximations for both simultaneous ruin probability and simultaneous ruin time for the two-dimensional Brownian risk model when the initial capital increases to infinity.

Keywords

two-dimensional Brownian risk modelBrownian motionsimultaneous ruin probabilitysimultaneous ruin timeruin time approximation

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 597 - 612
Copyright
© Applied Probability Trust 2020

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