A Gerber-Shiu Discounted Penalty Function in the Stationary Renewal Risk Process

2011 ◽  
pp. 198-201
Keyword(s):  
Penalty Function ◽  
Risk Process ◽  
Discounted Penalty Function ◽  
Renewal Risk

scholarly journals On a general class of renewal risk process: analysis of the Gerber-Shiu function

2005 ◽  
Vol 37 (03) ◽  
pp. 836-856 ◽  
Author(s):  
Shuanming Li ◽  
José Garrido
Keyword(s):  
Laplace Transform ◽  
Process Analysis ◽  
Risk Process ◽  
Expected Discounted Penalty Function ◽  
Renewal Equations ◽  
The Laplace Transform ◽  
Discounted Penalty Function ◽  
Renewal Risk ◽  
Defective Renewal Equations ◽  
Expected Discounted Penalty

We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a K n distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n ∈ N). The Laplace transform of the expected discounted penalty function at ruin is derived. This leads to a generalization of the defective renewal equations given by Willmot (1999) and Gerber and Shiu (2005). Finally, explicit results are given for rationally distributed claim severities.

The Gerber-Shiu Discounted Penalty Function for Risk Process with Double Markovian Environment

2010 ◽  
Vol 108-111 ◽  
pp. 1103-1108
Author(s):  
Wen Guang Yu
Keyword(s):  
Penalty Function ◽  
Risk Process ◽  
Closed Form Expression ◽  
Standard Wiener Process ◽  
Form Expression ◽  
Expected Discounted Penalty Function ◽  
Premium Rate ◽  
Special Cases ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

In this paper, we study the Gerber-Shiu discounted penalty function. We shall consider the case where the discount interest process and the occurrence of the claims are driven by two distinguished Markov process, respectively. Moreover, in this model we also consider the influence of a premium rate which varies with the level of free reserves. Using backward differential argument, we derive the integral equation satisfied by the expected discounted penalty function via differential argument when interest process in every state is perturbed by standard Wiener process and Poisson process. In some special cases, closed form expression for these quantities are obtained.

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