The Annals of Applied Probability

Classical solutions to reaction–diffusion systems for hedging problems with interacting Itô and point processes

Dirk Becherer and Martin Schweizer

Full-text: Open access

Abstract

We use probabilistic methods to study classical solutions for systems of interacting semilinear parabolic partial differential equations. In a modeling framework for a financial market with interacting Itô and point processes, such PDEs are shown to provide a natural description for the solution of hedging and valuation problems for contingent claims with a recursive payoff structure.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 2 (2005), 1111-1144.

Dates
First available in Project Euclid: 3 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1115137970

Digital Object Identifier
doi:10.1214/105051604000000846

Mathematical Reviews number (MathSciNet)
MR2134099

Zentralblatt MATH identifier
1075.60080

Subjects
Primary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60J25: Continuous-time Markov processes on general state spaces 91B28
Secondary: 60G44: Martingales with continuous parameter 60G55: Point processes 91B30: Risk theory, insurance

Keywords
Reaction–diffusion systems interacting processes recursive valuation hedging risk-minimization credit risk

Citation

Becherer, Dirk; Schweizer, Martin. Classical solutions to reaction–diffusion systems for hedging problems with interacting Itô and point processes. Ann. Appl. Probab. 15 (2005), no. 2, 1111--1144. doi:10.1214/105051604000000846. https://projecteuclid.org/euclid.aoap/1115137970


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