scholarly journals The Asymptotic Tail Behavior of Discounted Total Claims for a Bivariate Risk Model with Constant Rate of Interest

2017 ◽  
Author(s):  
Ying-hua DONG
Keyword(s):  
Risk Model ◽  
Tail Behavior ◽  
Constant Rate ◽  
Asymptotic Tail

SOME ADVANCES ON THE ERLANG(n) DUAL RISK MODEL

2014 ◽  
Vol 45 (1) ◽  
pp. 127-150 ◽  
Author(s):  
Eugenio V. Rodríguez-Martínez ◽  
Rui M. R. Cardoso ◽  
Alfredo D. Egídio dos Reis
Keyword(s):  
Risk Model ◽  
Waiting Times ◽  
Dual Model ◽  
Time Of Ruin ◽  
Constant Rate ◽  
Dual Risk Model ◽  
The Laplace Transform ◽  
The Time Of Ruin ◽  
Renewal Risk ◽  
The Individual

AbstractThe dual risk model assumes that the surplus of a company decreases at a constant rate over time and grows by means of upward jumps, which occur at random times and sizes. It is said to have applications to companies with economical activities involved in research and development. This model is dual to the well-known Cramér-Lundberg risk model with applications to insurance. Most existing results on the study of the dual model assume that the random waiting times between consecutive gains follow an exponential distribution, as in the classical Cramér-Lundberg risk model. We generalize to other compound renewal risk models where such waiting times are Erlang(n) distributed. Using the roots of the fundamental and the generalized Lundberg's equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Furthermore, we compute expected discounted dividends, as well as higher moments, when the individual common gains follow a Phase-Type, PH(m), distribution. We also perform illustrations working some examples for some particular gain distributions and obtain numerical results.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Tests of elliptical symmetry and the asymptotic tail behavior of the statistics

1999 ◽  
Vol 14 (4) ◽  
pp. 423-432
Author(s):  
Jing Ping ◽  
Zhu Lixing
Keyword(s):  
Tail Behavior ◽  
Elliptical Symmetry ◽  
Asymptotic Tail

scholarly journals Estimates for the Absolute Ruin Probability in the Compound Poisson Risk Model with Credit and Debit Interest

2008 ◽  
Vol 45 (03) ◽  
pp. 818-830 ◽  
Author(s):  
Jinxia Zhu ◽  
Hailiang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Absolute Ruin ◽  
Constant Rate ◽  
Negative Constant ◽  
The Absolute ◽  
Debit Interest ◽  
Poisson Risk Model

In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probability of this model. First we investigate the asymptotic behavior of the absolute ruin probability when the claim size distribution is light tailed. Then we study the case where the common distribution of claim sizes are heavy tailed.

scholarly journals On the joint distribution of tax payments and capital injections for a Lévy risk model

2018 ◽  
Vol 37 (2) ◽  
pp. 219-227
Author(s):  
Hansjörg Albrechter ◽  
Jevgienijs Ivanovs
Keyword(s):  
Explicit Formula ◽  
Joint Distribution ◽  
Net Present Value ◽  
Risk Model ◽  
Scale Function ◽  
Present Value ◽  
Constant Rate ◽  
Tax Payments ◽  
The One ◽  
Capital Injections

ON THE JOINT DISTRIBUTION OF TAX PAYMENTS AND CAPITAL INJECTIONS FOR A LÉVY RISK MODEL We study the joint distribution of tax payments according toa loss-carry-forward scheme and capital injections in a Lévy risk model, andprovide a transparent expression for the corresponding transform in terms ofthe scale function. This allows us to identify the net present value of capitalinjections in such a model, complementing the one for tax found in ourpaper [3]. We also apply the result to the situation when injections may be stopped at a constant rate, and in this case an explicit formula for the netpresent value of taxes and injections is given.

scholarly journals First-passage time asymptotics over moving boundaries for random walk bridges

2018 ◽  
Vol 55 (2) ◽  
pp. 627-651 ◽  
Author(s):  
Fiona Sloothaak ◽  
Vitali Wachtel ◽  
Bert Zwart
Keyword(s):  
Random Walk ◽  
Moving Boundary ◽  
First Passage Time ◽  
Passage Time ◽  
Finite Variance ◽  
Tail Behavior ◽  
First Passage ◽  
The Impact ◽  
Return Point ◽  
Asymptotic Tail

Abstract We study the asymptotic tail behavior of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -½, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the return point of the random walk bridge, leading to a possible phase transition depending on the order of the distance between zero and the moving boundary.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (2) ◽  
pp. 426-445 ◽  
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of rt+k and rt+1+⋯+rt+k when (rt)t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

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