A Note on Scale Functions and the Time Value of Ruin for Lévy Insurance Risk Processes
نویسندگان
چکیده
We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of Zhou (2005) we provide an explicit characterization of a generalized version of the Gerber-Shiu function in terms of scale functions, streamlining and extending results available in the literature.
منابع مشابه
On The Moments Of The Time To Ruin Distribution When The Initial Reserve Is Large And Claim Amount Distribution Is Two Stage Hypo Exponential Distribution
In any classical risk model one of the important random variable is time to ruin. As time to ruin warns the management for possible adverse situations that may arise, the distribution of time to ruin place a vital role in the day to day transactions of the any insurance company. Moments of the distribution are also important as coefficient of skewness of the distribution is very important in ac...
متن کاملDistribution of the Present Value of Dividend Payments in a Lévy Risk Model
In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.
متن کاملApplied Probability Trust (22 February 2007) DISTRIBUTION OF THE PRESENT VALUE OF DIVIDEND PAY- MENTS IN A LÉVY RISK MODEL
In this short paper, we show how uctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividend payments until ruin in a Lévy insurance risk model with a dividend barrier.
متن کاملRuin Probability with Parisian Delay for a Spectrally Negative Lévy Risk Process
In this paper we analyze the so-called Parisian ruin probability, which arises when the surplus process stays below 0 longer than a fixed amount of time ζ > 0. We focus on a general spectrally negative Lévy insurance risk process. For this class of processes, we derive an expression for the ruin probability in terms of quantities that can be calculated explicitly in many models. We find its Cra...
متن کاملApplying the Wiener-Hopf Monte Carlo Simulation Technique for Lévy processes to Path Functionals such as First Passage Times, Undershoots and Overshoots
In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Lévy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for instance in finance (the pricing of exotic options in a Lévy model) and insurance...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009