论文标题
相关布朗动作的有限时间破坏概率
Finite-time ruin probability for correlated Brownian motions
论文作者
论文摘要
令$（W_1（S），W_2（t）），S，T \ GE 0 $为双变量的Brownian运动，具有标准的Brownian运动边缘和恒定相关性$ρ\ in（-1,1）$，并定义了这两个上能力的共同生存概率， $π_ρ（C_1，C_2; U，V）= \ MathBb {P} \ left（\ sup_ {s s s \ in [0,1]} \ left（w_1（s）-c_1s \ oright）> ，$$，其中$ c_1，c_2 \ in \ mathbb {r} $和$ u，v $给出了正常数。 $π_ρ（C_1，C_2; U，V）$的近似值对于分析双变量Brownian风险模型以及双变量测试统计的研究而言是感兴趣的。在此贡献中，我们以$π_ρ（c_1，c_2; u，v）$得出紧密的界限。
Let $(W_1(s), W_2(t)), s,t\ge 0$ be a bivariate Brownian motion with standard Brownian motion marginals and constant correlation $ρ\in (-1,1)$ and define the joint survival probability of both supremum functionals $π_ρ(c_1,c_2; u, v)$ by $$π_ρ(c_1,c_2; u, v)=\mathbb{P}\left(\sup_{s \in [0,1]} \left(W_1(s)-c_1s\right)>u,\sup_{t \in [0,1]} \left(W_2(t)-c_2t\right)>v\right) ,$$ where $c_1,c_2 \in \mathbb{R}$ and $u,v$ are given positive constants. Approximation of $π_ρ(c_1,c_2; u, v) $ is of interest for the analysis of ruin probability in bivariate Brownian risk model as well as in the study of bivariate test statistics. In this contribution we derive tight bounds for $π_ρ(c_1,c_2; u, v)$ in the case $ρ\in (0,1)$ and obtain precise approximations by letting $u\to \infty$ and taking $v= au$ for some fixed positive constant $a$ and $ρ\in (-1,1).$
