Classical solutions to reaction-diffusion systems for hedging problems   with interacting Ito and point processes
  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 Ito 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. 
Dirk Becherer and Martin Schweizer