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Viscosity solutions of nonlinear integro-differential equations. (English) Zbl 0870.45002
The paper is concerned with existence and uniqueness of solutions to the following backward nonlinear integro-differential equation of the form \[ -\partial_t u(t,x)+F(t,x,u(t,x),Du(t,x),D^2 u(t,x)) -\int M(u(t,x+z),u(t,x))m_{t,x}(dz)=0 \] with \(u(T,x)\) given, where \(D\), \(D^2\) are space derivatives. The proof of existence is based on finding sub- and supersolutions and applying Perron’s method. The results find application in some problems of mathematical finance involving stochastic utility model.

45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
91B16 Utility theory
91B28 Finance etc. (MSC2000)
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