The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Informatica ◽  
2018 ◽  
Vol 29 (4) ◽  
pp. 733-756 ◽  
Author(s):  
Olga Navickienė ◽  
Jonas Sprindys ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Penalty Function ◽  
Risk Model ◽  
Discounted Penalty Function

scholarly journals Gerber-Shiu Function in a Discrete-time Risk Model with Dividend Strategy

2021 ◽  
pp. 97-110
Author(s):  
Junqing Huang ◽  
Zhenhua Bao
Keyword(s):  
General Theory ◽  
Discrete Time ◽  
Difference Equations ◽  
Penalty Function ◽  
Risk Model ◽  
Fundamental Equation ◽  
Numerical Examples ◽  
Premium Rate ◽  
Discounted Penalty Function ◽  
Constant Dividend Barrier

In this paper, a discrete-time risk model with dividend strategy and a general premium rate is considered. Under such a strategy, once the insurer’s surplus hits a constant dividend barrier , dividends are paid off to shareholders at  instantly. Using the roots of a generalization of Lundberg’s fundamental equation and the general theory on difference equations, two difference equations for the Gerber-Shiu discounted penalty function are derived and solved. The analytic results obtained are utilized to derive the probability of ultimate ruin when the claim sizes is a mixture of two geometric distributions. Numerical examples are also given to illustrate the applicability of the results obtained.

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