This book is focused on the recent developments on problems of probability model
uncertainty by using the notion of nonlinear expectations and, in particular, sublinear …

Conic optimization is a significant and thriving research area within the optimization
community. Conic optimization is the general class of problems concerned with optimizing a …

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 …

This book presents a radically new approach to problems of evaluating and optimizing the
performance of continuous-time stochastic systems. This approach is based on the use of a …

An elaborate discussion of the history and general features of the inventory problem may be
found in [2]. We shall content ourselves here with a brief description of the type of model …

In this book, we take the notion of nonlinear expectation as a fundamental notion of an
axiomatical system. This enables us to get directly many new and fundamental results: such …

Progress in the theory of economic equilibria and in game theory has proceeded hand in
hand with that of the mathematical tools used in the field, namely nonlinear analysis and, in …

This comprehensive volume on ergodic control for diffusions highlights intuition alongside
technical arguments. A concise account of Markov process theory is followed by a complete …

We consider in this chapter the optimal control of diffusions. Our objective is to derive the
various forms of the Stochastic Maximum Principle. The initial work of this area is due to HJ …

Introduction 1.1. Searching the Mechanism of Evaluations of Risky Assets 1.2. Axiomatic
Assumptions for Evaluations of Derivatives 1.3. Organization of the Lecture 2. Brownian …