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Ruin probability approximation for bidimensional Brownian risk model with tax

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  • Shashkov, Timofei

Abstract

Let B(t)=(B1(t),B2(t)), t≥0 be a two-dimensional Brownian motion with independent components and define the γ-reflected process X(t)=(X1(t),X2(t))=B1(t)−c1t−γ1infs1∈[0,t](B1(s1)−c1s1),B2(t)−c2t−γ2infs2∈[0,t](B2(s2)−c2s2),with given finite constants c1,c2∈R and γ1,γ2∈[0,2). The goal of this paper is to derive the asymptotics of the ruin probability P∃t∈[0,T]:X1(t)>u,X2(t)>auas u→∞ for T>0.

Suggested Citation

  • Shashkov, Timofei, 2025. "Ruin probability approximation for bidimensional Brownian risk model with tax," Statistics & Probability Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:stapro:v:217:y:2025:i:c:s0167715224002748
    DOI: 10.1016/j.spl.2024.110305
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    References listed on IDEAS

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    1. 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.
    2. Hashorva, Enkelejd, 2019. "Approximation of some multivariate risk measures for Gaussian risks," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 330-340.
    3. Grigori Jasnovidov, 2020. "Approximation of ruin probability and ruin time in discrete Brownian risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(8), pages 718-735, September.
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