Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach
نویسنده
چکیده
This paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the finite time (and ultimate) ruin probabilities, the distribution of the ruin severity, the reserves prior to ruin, and the Laplace transform of the ruin time. Interestingly, the usual net profit condition will be essentially relaxed. Most results generalize those known for the compound Poisson claim process.
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 کاملAsymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
This paper mainly considers a nonstandard risk model with a constant interest rate, where both the claim sizes and the inter-arrival times follow some certain dependence structures. When the claim sizes are dominatedly varying-tailed, asymptotics for the infinite time ruin probability of the above dependent risk model have been given.
متن کاملOn Simple Ruin Expressions in Dependent Sparre Andersen Risk Models
In this note we provide a simple alternative derivation of an explicit formula of Kwan and Yang [14] for the probability of ruin in a risk model with a certain dependence between general claim inter-occurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probabil...
متن کاملSample path behavior of a Lévy insurance risk process approaching ruin, under the Cramér-Lundberg and convolution equivalent conditions
Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a Lévy insurance risk process under the Cramér-Lundberg and convolution equivalent conditions. For example the limiting distributions of the overshoot and the undershoot are strikingly similar in these two settings. This is somewhat surprising since the global sample path behavior of the proces...
متن کاملA Functional Limit Theorem for Stochastic Integrals Driven by a Time-changed Symmetric Α-stable Lévy Process
Under proper scaling and distributional assumptions, we prove the convergence in the Skorokhod space endowed with the M1-topology of a sequence of stochastic integrals of a deterministic function driven by a time-changed symmetric α-stable Lévy process. The time change is given by the inverse β-stable subordinator.
متن کامل