Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach

@article{Benth2001OptimalPS,
  title={Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach},
  author={Fred E. Benth and Kenneth H. Karlsen and Kristin Reikvam},
  journal={Finance and Stochastics},
  year={2001},
  volume={5},
  pages={275-303}
}
We study a problem of optimal consumption and portfolio selection in a market where the logreturns of the uncertain assets are not necessarily normally distributed. The natural models then involve pure-jump L evy processes as driving noise instead of Brownian motion like in the Black and Scholes model. The state constrained optimization problem involves the notion of local substitution and is of singular type. The associated Hamilton-Jacobi-Bellman equation is a nonlinear rst order integro… CONTINUE READING
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