Chebyshev polynomial approximation for high-order partial differential equations with complicated conditions

2009 ◽  
Vol 25 (3) ◽  
pp. 610-621 ◽  
Author(s):  
Aysegül Akyüz-Dascioglu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Chebyshev Polynomial ◽  
Polynomial Approximation ◽  
High Order ◽  
Partial Differential ◽  
Chebyshev Polynomial Approximation ◽  
Complicated Conditions

scholarly journals Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Chebyshev Polynomial ◽  
Polynomial Approximation ◽  
Risk Model ◽  
Arbitrary Distribution ◽  
System Of Differential Equations ◽  
Numerical Result ◽  
Chebyshev Polynomial Approximation ◽  
Markov Modulated

This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.

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