Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends
نویسندگان
چکیده
We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.
منابع مشابه
Algorithmic 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 کاملStructural 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 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 orderings and bounds in a generalized Sparre Andersen risk model
A generalization of the Gerber-Shiu function proposed by Cheung et al. (2009a) is used to derive some ordering properties for certain ruin-related quantities in a Sparre Andersen type risk model. Additional bounds and/or refinements can be obtained by further assuming that the claim size and the interclaim time distributions possess certain reliability properties. Finally, numerical examples ar...
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 کامل