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Full-Text Articles in Physical Sciences and Mathematics
An Optimal Execution Problem With S-Shaped Market Impact Functions, Takashi Kato
An Optimal Execution Problem With S-Shaped Market Impact Functions, Takashi Kato
Communications on Stochastic Analysis
No abstract provided.
Numerical Methods For Hamilton-Jacobi-Bellman Equations, Constantin Greif
Numerical Methods For Hamilton-Jacobi-Bellman Equations, Constantin Greif
Theses and Dissertations
In this work we considered HJB equations, that arise from stochastic optimal control problems
with a finite time interval. If the diffusion is allowed to become degenerate, the solution cannot be
understood in the classical sense. Therefore one needs the notion of viscosity solutions. With some
stability and consistency assumptions, monotone methods provide the convergence to the viscosity
solution. In this thesis we looked at monotone finite difference methods, semi lagragian methods and
finite element methods for isotropic diffusion. In the last chapter we introduce the vanishing moment
method, a method not based on monotonicity.