“The Time Value of Ruin in a Sparre Andersen Model,’ Hans U. Gerber and Elias S. W. Shiu, April 2005
نویسندگان
چکیده
منابع مشابه
Structural properties of Gerber–Shiu functions in dependent Sparre Andersen models
Available online xxxx Keywords: Defective renewal equation Compound geometric distribution Ladder height Lundberg's fundamental equation Generalized adjustment coefficient Cramer's asymptotic ruin formula Esscher transform Last interclaim time NWU NBU a b s t r a c t The structure of various Gerber–Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and...
متن کاملOn the ruin time distribution for a Sparre Andersen process with exponential claim sizes
We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. [7] for such processes with Erlang inter-claim times. We illustrate our result in the cases of gamma and mixed exponential inter-claim time distributions.
متن کاملThe Joint Density of the Surplus before and after Ruin in the Sparre Andersen Model
Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber–Shiu...
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 کاملAlgorithmic analysis of the Sparre Andersen model in discrete time
In this paper, we show that the delayed Sparre Andersen insurance risk model in discrete time can be analyzed as a doubly infinite, right skip-free Markov chain. We then describe how matrix analytic methods can be used to establish a computational procedure for calculating the probability distributions associated with fundamental ruin-related quantities of interest, such as the time of ruin, th...
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: North American Actuarial Journal
سال: 2005
ISSN: 1092-0277,2325-0453
DOI: 10.1080/10920277.2005.10596232