This is a substantial revision of the previous edition with added new material. The
presentation of Chapter 6 is updated. In particular the Interchangeability Principle for risk …

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 …

We introduce the concept of a Markov risk measure and we use it to formulate risk-averse
control problems for two Markov decision models: a finite horizon model and a discounted …

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 …

In this paper we give some basic and important properties of several typical Banach spaces
of functions of G-Brownian motion paths induced by a sublinear expectation—G-expectation …

This book is the first in the market to treat single-and multi-period risk measures (risk
functionals) in a thorough, comprehensive manner. It combines the treatment of properties of …

We extend the definition of a convex risk measure to a conditional framework where
additional information is available. We characterize these risk measures through the …

We study dynamic monetary risk measures that depend on bounded discrete-time
processes describing the evolution of financial values. The time horizon can be finite or …

This paper shows how g-expectations and conditional g-expectations provide some families
of static and dynamic risk measures. Conversely, some sufficient conditions for a dynamic …

This is the first book about the emerging field of utility indifference pricing for valuing
derivatives in incomplete markets. René Carmona brings together a who's who of leading …