Viscosity solutions of nonlinear integro-differential equations (Q1814669)
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scientific article; zbMATH DE number 939889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Viscosity solutions of nonlinear integro-differential equations |
scientific article; zbMATH DE number 939889 |
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Viscosity solutions of nonlinear integro-differential equations (English)
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12 December 1996
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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.
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backward nonlinear integro-differential equation
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sub- and supersolutions
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Perron's method
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mathematical finance
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stochastic utility model
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viscosity solutions
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