Uniqueness of the Solution to a Difference-Partial Differential Equation for Finance

2003 ◽  
Vol 13 (07) ◽  
pp. 919-943
Author(s):  
C. Mancini
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rate ◽  
Jump Diffusion ◽  
Market Model ◽  
Contingent Claim ◽  
Partial Differential ◽  
Financial Model ◽  
Diffusion Modelling ◽  
Uniqueness Of The Solution

In this paper we study a difference partial differential equation, arising from a financial model, whose solution represents the price of a security linked to a dividend-paying stock. The market model consists of a jump-diffusion process modelling the stock evolution and an independent diffusion modelling the stochastic spot interest rate. We establish the desirable property of the uniqueness of solution to the equation and, since the specialized model is complete, we can consistently price any contingent claim.

Non-Uniqueness of The Solution to a Generalized Dirichlet Problem

1974 ◽  
Vol 17 (4) ◽  
pp. 605-606
Author(s):  
E. L. Koh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Unique Solution ◽  
Partial Differential ◽  
Uniqueness Of The Solution ◽  
Image Position ◽  
Generalized Dirichlet

It is generally known [1] that the singular partial differential equationmay not have a unique solution because of the existence of nontrivial representations of zero.1

MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (02) ◽  
pp. 271-294 ◽  
Author(s):  
B. BOUFOUSSI ◽  
N. MRHARDY
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Partial Differential Equation ◽  
Yosida Approximation ◽  
Partial Differential ◽  
Doubly Stochastic ◽  
Uniqueness Of The Solution

In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.

Convergence and Error Analysis of Series Solution of Nonlinear Partial Differential Equation

2018 ◽  
Vol 7 (4) ◽  
pp. 303-308 ◽  
Author(s):  
Prince Singh ◽  
Dinkar Sharma
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Error Analysis ◽  
Series Solution ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Uniqueness Of The Solution ◽  
Established Fact ◽  
Sumudu Transforms

Abstract A hybrid method of Sumudu transforms and homotopy perturbation method (HPM) is used to solve nonlinear partial differential equation. Here the nonlinear terms are handled with He’s polynomial to obtain the series solution. But, for the authenticity of the obtained solution, the condition of convergence and uniqueness of the solution is derived. The facts are obtained in reference to convergence and error analysis of this solution. Finally, the established fact is supported by finding solution of two well known equations Newell-Whitehead Segel and Fisher’s equation

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