scholarly journals On a perturbed Sparre Andersen risk model with threshold dividend strategy and dependence

2014 ◽  
Vol 255 ◽  
pp. 248-269 ◽  
Author(s):  
Zhimin Zhang
Keyword(s):  
Risk Model ◽  
Threshold Dividend Strategy ◽  
Sparre Andersen Risk Model

scholarly journals Ruin Probabilities for Two Classes of Risk Processes

2005 ◽  
Vol 35 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Shuanming Li ◽  
José Garrido
Keyword(s):  
Laplace Transform ◽  
Ruin Probability ◽  
Risk Model ◽  
Compound Poisson Process ◽  
Ruin Probabilities ◽  
Counting Processes ◽  
Arrival Times ◽  
The Laplace Transform ◽  
Sparre Andersen Risk Model ◽  
Risk Processes

We consider a risk model with two independent classes of insurance risks. We assume that the two independent claim counting processes are, respectively, Poisson and Sparre Andersen processes with generalized Erlang(2) claim inter-arrival times. The Laplace transform of the non-ruin probability is derived from a system of integro-differential equations. Explicit results can be obtained when the initial reserve is zero and the claim severity distributions of both classes belong to the Kn family of distributions. A relation between the ruin probability and the distribution of the supremum before ruin is identified. Finally, the Laplace transform of the non-ruin probability of a perturbed Sparre Andersen risk model with generalized Erlang(2) claim inter-arrival times is derived when the compound Poisson process converges weakly to a Wiener process.

scholarly journals The Perturbed Dual Risk Model with Constant Interest and a Threshold Dividend Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Fanzi Zeng ◽  
Jisheng Xu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Present Value ◽  
Numerical Examples ◽  
Threshold Dividend Strategy ◽  
Absolute Ruin ◽  
Dual Risk Model ◽  
The Moment ◽  
The Impact ◽  
Constant Interest

We consider the perturbed dual risk model with constant interest and a threshold dividend strategy. Firstly, we investigate the moment-generation function of the present value of total dividends until ruin. Integrodifferential equations with certain boundary conditions are derived for the present value of total dividends. Furthermore, using techniques of sinc numerical methods, we obtain the approximation results to the expected present value of total dividends. Finally, numerical examples are presented to show the impact of interest on the expected present value of total dividends and the absolute ruin probability.

scholarly journals The Absolute Ruin Insurance Risk Model with a Threshold Dividend Strategy

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 377 ◽  
Author(s):  
Wenguang Yu ◽  
Yujuan Huang ◽  
Chaoran Cui
Keyword(s):  
Risk Model ◽  
Insurance Companies ◽  
Insurance Company ◽  
Insurance Risk ◽  
Threshold Dividend Strategy ◽  
Dividend Payments ◽  
Absolute Ruin ◽  
The Absolute ◽  
Debit Interest ◽  
Insurance Risk Model

The absolute ruin insurance risk model is modified by including some valuable market economic information factors, such as credit interest, debit interest and dividend payments. Such information is especially important for insurance companies to control risks. We further assume that the insurance company is able to finance and continue to operate when its reserve is negative. We investigate the integro-differential equations for some interest actuarial diagnostics. We also provide numerical examples to explain the effects of relevant parameters on actuarial diagnostics.

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