ABSTRACT
In this chapter we review basic general properties of nonlinear second order parabolic PDEs. As a consequence of the comparison principle, these equations 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 Although proofs have been replaced by appropriate references such as [21, 24], we strive to give some mathematical intuition.
