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Simultaneous ruin probability for multivariate Gaussian risk model

Author

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  • Bisewski, Krzysztof
  • Dȩbicki, Krzysztof
  • Kriukov, Nikolai

Abstract

Let Z(t)=(Z1(t),…,Zd(t))⊤,t∈R where Zi(t),t∈R, i=1,…,d are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For X(t)=AZ(t),t∈R, where A is a nonsingular d×d real-valued matrix, u,c∈Rd and T>0 we derive tight bounds for P∃t∈[0,T]:∩i=1d{Xi(t)−cit>ui}and find exact asymptotics as (u1,…,ud)⊤=(ua1,…,uad)⊤ for any (a1,…,ad)⊤∈Rd∖(−∞,0]d and u→∞.

Suggested Citation

  • Bisewski, Krzysztof & Dȩbicki, Krzysztof & Kriukov, Nikolai, 2023. "Simultaneous ruin probability for multivariate Gaussian risk model," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 386-408.
    • Handle: RePEc:eee:spapps:v:160:y:2023:i:c:p:386-408
    DOI: 10.1016/j.spa.2023.03.002
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    2. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Wang, Longmin, 2020. "Extremes of vector-valued Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5802-5837.
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    5. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Ji, Lanpeng & Tabiś, Kamil, 2015. "Extremes of vector-valued Gaussian processes: Exact asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4039-4065.
    6. Hüsler, J. & Piterbarg, V., 2004. "On the ruin probability for physical fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 315-332, October.
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