scholarly journals Option Pricing under Risk-Minimization Criterion in an Incomplete Market with the Finite Difference Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xinfeng Ruan ◽  
Wenli Zhu ◽  
Shuang Li ◽  
Jiexiang Huang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Incomplete Market ◽  
Martingale Measure ◽  
Risk Minimization ◽  
European Option ◽  
The Finite Difference Method ◽  
Nikodym Derivative

We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE) of European option. The finite difference method is employed to compute the European option valuation of PIDE.

Study and Simulate the Air Pollution Based on the Finite Difference Method

2012 ◽  
Vol 518-523 ◽  
pp. 2820-2824
Author(s):  
Yi Ni Guo ◽  
Yan Zhang ◽  
Jian Wang ◽  
Ye Huang
Keyword(s):  
Finite Element Method ◽  
Air Pollution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
The Finite Element Method ◽  
Liquid Diffusion ◽  
Continuous Problems ◽  
The Finite Difference Method ◽  
The Difference

The finite difference method that is the finite element method is used to solve the plane continuous problems. In this article, the theory and method of the finite difference method, as well as the application on the boundary problem are introduced. By analyzing the potential flew field equation and liquid diffusion equation, they are discreted using the difference method and the numerical analysis under certain boundary condition is conducted. In air pollution, the smoke in the diffusion is typical planar continuous problems. In this paper, the finite difference method is used to analyse and simulate the spread of the smoke.

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