Existence & Regularity of Weak Solutions of Degenerate Parabolic PDE Models for the Pricing of Security Derivatives

2009/02/10 by Rasoul Behboudi, Behboudi, Rasoul, You-lan Zhu +1
Mathematics · #Analysis of PDEs (math.AP) #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Numerical Analysis (math.NA) #advanced mathematical theories

paper · doi:10.48550/arxiv.0902.1721

openalex publication_date 2009/02/10 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative properties of solutions of such equations. The generalized solvability for such models with degeneracy at the boundaries is proven by employing solutions obtained from finite difference numerical schemes. Furthermore, the regularity of such solutions is studied.

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