 Abstract:
An original method to solve Optimal Stopping Problems coming from Mathematical Finance is presented. This paper fully reviews the one dimensional case, from the continuous
to the numerical and algorithmic point of view.
From a continuous point of view, this method can be classifi ed as a quantized method,
usually considered as a Stochastic
approach. However, we will be relying heavily over Partial
Di fferential Equation (PDE) arguments. Thus, this method may be considered as an hybrid
Stochastic / PDE one. From a numerical point of view, these schemes belong to the class of
"Optimally Transported Schemes".
The overall methodology proposed in this paper eases the code production, allow to design
faster and more accurate algorithms, gives a natural setting to the calibration problem, provide
a uni fied stochastic/PDE computational framework for Financial engineering
in one
dimension, and, finally, should be a good candidate to break the "Curse of Dimensions".
Authors:
Jean-Marc MERCIER
JEL classification:
C61 C63
Keywords:
Optimally Transported Schemes; Monte Carlo; Calibration; Optimal Stopping poblems
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