On a Risk Model with Dependence between Claim Sizes and Claim Intervals under a Linear Dividend Barrier and Stochastic Interest

Linearly Independent ◽

Stochastic Interest ◽

Discounted Penalty Function

The risk model with interclaim-dependent claim sizes is studied in the presence of a linear dividend barrier and stochastic interest. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber-Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation.

On a Risk Model with Dependence between Interclaim Arrivals and Claim Sizes with Multiple Thresholds under Stochastic Interest

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.179-180.1086 ◽

2011 ◽

Vol 179-180 ◽

pp. 1086-1090 ◽

Cited By ~ 1

Author(s):

Yu Juan Huang ◽

Ai Qin Li

Keyword(s):

Differential Equation ◽

Risk Model ◽

Penalty Functions ◽

Multiple Thresholds ◽

Stochastic Interest

The risk model with dependence between interclaim arrivals and claim sizes is studied in the presence of multiple thresholds and stochastic interest. An integro-differential equation for some Gerber-Shiu discounted penalty functions is derived.

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

Mathematical Problems in Engineering ◽

10.1155/2014/450149 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 2

Author(s):

Yujuan Huang ◽

Wenguang Yu

Keyword(s):

Differential Equation ◽

Exponential Distribution ◽

Penalty Function ◽

Risk Model ◽

Numerical Example ◽

N Distribution ◽

Constant Dividend Barrier ◽

Sparre Andersen Risk Model

This paper constructs a Sparre Andersen risk model with a constant dividend barrier in which the claim interarrival distribution is a mixture of an exponential distribution and an Erlang(n) distribution. We derive the integro-differential equation satisfied by the Gerber-Shiu discounted penalty function of this risk model. Finally, we provide a numerical example.

2011 International Conference on Control, Automation and Systems Engineering (CASE) ◽

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

10.1109/iccase.2011.5997565 ◽

2011 ◽

Author(s):

Yi Zhang

Keyword(s):

Differential Equation ◽

Penalty Function ◽

Expected Discounted Penalty Function ◽

Expected Discounted Penalty

The Markov Risk Model under Stochastic Discount Interest Force

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.179-180.1080 ◽

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 ◽

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.29-32.1150 ◽

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 ◽

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.