摘要
For a risk process R_u(t) = u + ct- X(t), t≥0, where u≥0 is the initial capital, c > 0 is the premium rate and X(t), t≥0 is an aggregate claim process, we investigate the probability of the Parisian ruin P_S(u, T_u) = P{inf (t∈[0,S]_(s∈[t,t+T_u])) sup R_u(s) < 0}, S, T_u > 0.For X being a general Gaussian process we derive approximations of P_S(u, T_u) as u →∞. As a by-product, we obtain the tail asymptotic behaviour of the infimum of a standard Brownian motion with drift over a finite-time interval.
For a risk process R_u（t） = u ＋ ct- X（t）, t≥0, where u≥0 is the initial capital, c 〉 0 is the premium rate and X（t）, t≥0 is an aggregate claim process, we investigate the probability of the Parisian ruin P_S（u, T_u） = P{inf （t∈[0,S]_（s∈[t,t＋T_u]）） sup R_u（s） 〈 0}, S, T_u 〉 0.For X being a general Gaussian process we derive approximations of P_S（u, T_u） as u →∞. As a by-product, we obtain the tail asymptotic behaviour of the infimum of a standard Brownian motion with drift over a finite-time interval.
基金
the Swiss National Science Foundation (Grant No. 200021140633/1)
the project Risk Analysis, Ruin and Extremes (an FP7 Marie Curie International Research Staff Exchange Scheme Fellowship) (Grant No. 318984)
Narodowe Centrum Nauki (Grant No. 2013/09/B/ST1/01778 (2014-2016))
关键词
时间跨度
巴黎
漂移布朗运动
破产概率
时间间隔
渐近行为
副产品
高斯
Parisian ruin Gaussian process Lévy process fractional Brownian motion infimum of Brownian motion generalized Pickands constant generalized Piterbarg constant
