The Application of the Extended Generator in Deriving the Integro-Differential Equation Satisfied by the Expected Discounted Penalty Function

2011 ◽  
Author(s):  
Yi Zhang
Keyword(s):  
Differential Equation ◽  
Penalty Function ◽  
Expected Discounted Penalty Function ◽  
Integro Differential Equation ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

The Markov Risk Model under Stochastic Discount Interest Force

2011 ◽  
Vol 179-180 ◽  
pp. 1080-1085
Author(s):  
Yu Juan Huang ◽  
Chun Ming Zhang
Keyword(s):  
Differential Equation ◽  
Penalty Function ◽  
Risk Model ◽  
Standard Wiener Process ◽  
Exponential Distributions ◽  
Expected Discounted Penalty Function ◽  
Geometric Process ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

We investigate the expected discounted penalty function in which the discount interest process is driven by markov process. We obtain the integro-differential equation satisfied by the expected discounted penalty function when interest process is perturbed by standard Wiener process and Poisson-Geometric process. A system of Laplace transforms of the expected discounted penalty function, given the initial environment state, is established from a system of integro-differential equations. One example is given with claim sizes that have exponential distributions.

The Expected Discounted Penalty Function under Stochastic Discount Interest Force Driven by Markov Process

2012 ◽  
Vol 433-440 ◽  
pp. 5035-5039
Author(s):  
Chun Ming Zhang
Keyword(s):  
Differential Equation ◽  
Markov Process ◽  
Penalty Function ◽  
Standard Wiener Process ◽  
Exponential Distributions ◽  
Expected Discounted Penalty Function ◽  
Geometric Process ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

We investigate the expected discounted penalty function in which the discount interest process is driven by markov process. We obtain the integro-differential equation satisfied by the expected discounted penalty function when interest process is perturbed by standard Wiener process and Poisson-Geometric process. A system of Laplace transforms of the expected discounted penalty function, given the initial environment state, is established from a system of integro-differential equations. One example is given with claim sizes that have exponential distributions.

Improvement to the Expected Discounted Penalty Function for a Classical Risk Model with a Threshold Dividend Strategy

2010 ◽  
Vol 29-32 ◽  
pp. 1150-1155
Author(s):  
Wen Guang Yu ◽  
Zhi Liu
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Penalty Function ◽  
Risk Model ◽  
Classical Risk Model ◽  
Expected Discounted Penalty Function ◽  
Threshold Dividend Strategy ◽  
Interest Force ◽  
Discounted Penalty Function ◽  
Expected Discounted Penalty

In this paper, we study the expected discounted penalty function for a classical risk model in which a threshold dividend strategy is used for a classical risk model and the discount interest force process is not a constant, but a stochastic process driven by Poisson process and Wiener process. In this model, we derive and solve an integro-differential equation for the expected discounted penalty function.

scholarly journals Perturbed MAP Risk Models with Dividend Barrier Strategies

2009 ◽  
Vol 46 (2) ◽  
pp. 521-541 ◽  
Author(s):  
Eric C. K. Cheung ◽  
David Landriault
Keyword(s):  
Penalty Function ◽  
Risk Model ◽  
Arrival Process ◽  
Risk Models ◽  
Expected Discounted Penalty Function ◽  
Numerical Examples ◽  
Dividend Payments ◽  
Discounted Penalty Function ◽  
Markov Modulated ◽  
Expected Discounted Penalty

In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

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