December 2013
Intermediate to advanced
484 pages
14h 54m
English
Content preview from Nonlinear Option Pricing
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Chapter 4
Nonlinear PDEs: A Bit of Theory
La finance est d´ecrite par des EDPs paraboliques non-lin´eaires et
cela n’a rien `a voir avec le mouvement brownien.
1
— Pierre-Louis Lions, cours du Coll`ege de France (2007)
In this chapter we review basic general properties of nonlinear second order
parabolic PDEs. As a consequence of the comparison principle, these equa-
tions naturally show up in finance. Since many nonlinear PDEs arising in
finance are of the Hamilton-Jacobi-Bellman type, we present a crash course
on stochastic control theory highlighting the main notions and results such
as verification theorems and viscosity solutions. Although proofs hav ...
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