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

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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

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

First available in Project Euclid: 3 May 2005

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Zentralblatt MATH identifier

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

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


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.

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