This paper surveys the most recent advances in the context of decision making under
uncertainty, with an emphasis on the modeling of risk-averse preferences using the …

Risk measures are used not only for financial institutions' internal risk management but also
for external regulation (eg, in the Basel Accord for calculating the regulatory capital …

This book provides the most comprehensive treatment of the theoretical concepts and
modelling techniques of quantitative risk management. Whether you are a financial risk …

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 …

Fix a domain\mathcal S ⊂ R^ k (our solvency region) and let Y (t)= Y^(u)(t) be a stochastic
process of the form d Y (t) &= b (Y (t), u (t)) d t+ σ (Y (t), u (t)) d B (t)\nonumber\&\quad+ ∫ …

This book gives an introduction to basic concepts and methods in mathematical risk
analysis, in particular to those parts of risk theory which are of particular relevance in finance …

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 …

Contains Nearly 100 Pages of New MaterialThe recent financial crisis has shown that credit
risk in particular and finance in general remain important fields for the application of …

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 …