Some Remarks on Delayed Renewal Risk Models

2010 ◽  
Vol 40 (1) ◽  
pp. 199-219 ◽  
Author(s):  
Jae-Kyung Woo
Keyword(s):  
Present Model ◽  
Time Dependent ◽  
Alternative Methods ◽  
Asymptotic Formulas ◽  
Claim Size ◽  
Risk Models ◽  
Independence Assumption ◽  
Renewal Risk ◽  
Delayed Model ◽  
Special Case

AbstractSome extensions to the delayed renewal risk models are considered. In particular, the independence assumption between the interclaim time and the subsequent claim size is relaxed, and the classical Gerber-Shiu penalty function is generalized by incorporating more variables. As a result, general structures regarding various joint densities of ruin related quantities as well as their probabilistic interpretations are provided. The numerical example in case of time-dependent claim sizes is provided, and also the usual delayed model with time-independent claim sizes is discussed including a special case with exponential claim sizes. Furthermore, asymptotic formulas for the associated compound geometric tail for the present model are derived using two alternative methods.

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

2007 ◽  
Vol 55 (4) ◽  
pp. 207-222 ◽  
Author(s):  
Soohan Ahn ◽  
Andrei L. Badescu ◽  
V. Ramaswami
Keyword(s):  
Fluid Flows ◽  
Time Dependent ◽  
Finite Buffer ◽  
Risk Models ◽  
Time Dependent Analysis

scholarly journals Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Erdoğan Şen ◽  
Jong Jin Seo ◽  
Serkan Araci
Keyword(s):  
Boundary Value Problem ◽  
Liouville Operator ◽  
Liouville Problem ◽  
Asymptotic Formulas ◽  
Retarded Argument ◽  
Eigenvalues And Eigenfunctions ◽  
Transmission Coefficients ◽  
Discontinuous Boundary ◽  
Sturm Liouville ◽  
Special Case

In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the first work containing two discontinuities points in the theory of differential equations with retarded argument. In that special case the transmission coefficients and retarded argument in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

A general time-dependent invariant for and integrability of the quadratic system

1994 ◽  
Vol 444 (1922) ◽  
pp. 643-650 ◽  
Keyword(s):  
Direct Method ◽  
First Integral ◽  
Quadratic System ◽  
Time Dependent ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Linear Polynomial ◽  
A Direct Method ◽  
Special Case ◽  
General Time

We derive a general time-dependent invariant (first integral) for the quadratic system (QS) that requires only one condition on the coefficients of the QS. The general invariant could yield asymptotic behaviour of phase-space trajectories. With more conditions imposed on the coefficients, the general invariant reduces to polynomial form and is equivalent to polynomial invariants found using a direct method. For the special case of a linear polynomial invariant where one of the variables is analytically invertible, the solution of the QS is reduced to a quadrature.

scholarly journals Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models

2011 ◽  
Vol 48 (A) ◽  
pp. 3-14
Author(s):  
Hansjörg Albrecher ◽  
Sem C. Borst ◽  
Onno J. Boxma ◽  
Jacques Resing
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Risk Models ◽  
Renewal Risk Model ◽  
Insurance Portfolio ◽  
Tax Payments ◽  
Renewal Risk

In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramér–Lundberg model with and without tax payments. We also provide a relation of the Cramér–Lundberg risk model with the G/G/∞ queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramér– Lundberg risk model.

scholarly journals A note on compound renewal risk models with dependence

2015 ◽  
Vol 285 ◽  
pp. 295-311 ◽  
Author(s):  
Hélène Cossette ◽  
Etienne Larrivée-Hardy ◽  
Etienne Marceau ◽  
Julien Trufin
Keyword(s):  
Risk Models ◽  
Renewal Risk

Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

2010 ◽  
Vol 42 (4) ◽  
pp. 1126-1146 ◽  
Author(s):  
Jinzhu Li ◽  
Qihe Tang ◽  
Rong Wu
Keyword(s):  
Asymptotic Formula ◽  
Risk Model ◽  
Tail Probability ◽  
Dependence Structure ◽  
Claim Size ◽  
Claim Size Distribution ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
The Impact

Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.

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