RATIO MONOTONICITY FOR TAIL PROBABILITIES IN THE RENEWAL RISK MODEL
نویسندگان
چکیده
منابع مشابه
Ratio Monotonicity for Tail Probabilities in the Renewal Risk Model
A renewal model in risk theory is considered, where H(u, y) is the tail of the distribution of the deficit at ruin with initial surplus u and F(y) is the tail of the ladder height distribution. Conditions are derived under which the ratio H(u, y)/F(u + y) is nondecreasing in u for any y ≥ 0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then...
متن کاملRuin Probabilities for Large Claims in Delayed Renewal Risk Model*
The following stochastic model, which can be used for example to describe an insurance business, has been considered by Grandell (1991) and Embrechts et al. (1997), Rolski et al. (1999) and Asmussen (2000), among others. Costs of claims Zi, ib 1, form a sequence of independent and identically distributed (i.i.d.), positive random variables (r.v.s) with a common distribution function (d.f.) F an...
متن کاملStationary Tail Probabilities in Exponential Server Tandems with Renewal Arrivals
The problem considered is that of estimating the tail stationary probability for two exponential server queues in series fed by renewal arrivals. We compute the tail of the marginal queue length distribution at the second queue. The marginal at the first queue is known by the classical result for the GI/M/1 queue. The approach involves deriving necessary and sufficient conditions on the paths o...
متن کاملUniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model
Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same...
متن کاملWorst - Case Tail Probabilities in Credit Risk
Simulation is widely used to measure credit risk in portfolios of loans, bonds, and other instruments subject to possible default. This analysis requires performing the difficult modeling task of capturing the dependence between obligors adequately. Current methods assume a form for the joint distribution of the obligors and match its parameters to given dependence specifications, usually corre...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability in the Engineering and Informational Sciences
سال: 2011
ISSN: 0269-9648,1469-8951
DOI: 10.1017/s0269964810000331