We investigate comparison and existence results for viscosity solutions of fully nonlinear,
second-order, elliptic, possibly degenerate equations. These results complement those …

These lectures present the most basic theory of" viscosity solutions" of fully nonlinear scalar
partial differential equations of first and second order. Other contributions to this volume …

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of
second order provides a framework in which startling comparison and uniqueness …

This book is an introduction to optimal stochastic control for continuous time Markov
processes and the theory of viscosity solutions. It covers dynamic programming for …

Stochastic optimization problems arise in decision-making problems under uncertainty, and
find various applications in economics and finance. On the other hand, problems in finance …

The goal of the book is to extend classical regularity theorems for solutions of linear elliptic
partial differential equations to the context of fully nonlinear elliptic equations. This class of …

We present a simple, purely analytic method for proving the convergence of a wide class of
approximation schemes to the solution of fully non linear second-order elliptic or parabolic …

We construct a unique weak solution of the nonlinear PDE which asserts each level set
evolves in time according to its mean curvature. This weak solution allows us then to define …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

The study of complex Monge–Ampere equations on compact Kähler manifolds is an
important part of the interface between complex analysis and differential geometry …