On the viscosity solutions of a stochastic differential utility problem

  title={On the viscosity solutions of a stochastic differential utility problem},
  author={Fabio Antonelli and Andrea Pascucci},
We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for the following equation in R: @xxu þ u@yu @tu 1⁄4 f ð ; uÞ; where f is Lipschitz continuous. We also characterize the solution in the vanishing viscosity sense. r 2002 Elsevier Science (USA). All rights reserved. 

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