VISCOSITY SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS

Authors
ALVAREZ O TOURIN A
Citation
O. Alvarez et A. Tourin, VISCOSITY SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS, Annales de l Institut Henri Poincare. Analyse non lineaire, 13(3), 1996, pp. 293-317
Citations number
12
Categorie Soggetti
Mathematics,Mathematics
Journal title
Annales de l Institut Henri Poincare. Analyse non lineaire → ACNP
ISSN journal
02941449
Volume
13
Issue
3
Year of publication
1996
Pages
293 - 317
Database
ISI
SICI code
0294-1449(1996)13:3<293:VSONIE>2.0.ZU;2-G
Abstract
We investigate the questions of the existence and uniqueness of viscos ity solutions to the Cauchy problem for integro-differential PDEs with nonlinear integral term. The existence of a solution is established b y considering semicontinuous subsolutions and supersolutions and apply ing Perron's method. Uniqueness is proved for both bounded and unbound ed solutions. These results are then applied to a problem arising in F inance, namely the stochastic differential utility model under mixed P oisson-Brownian information.