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 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 …

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 …

We discuss a number of quantile‐based risk measures (QBRMs) that have recently been
developed in the financial risk and actuarial/insurance literatures. The measures considered …

We investigate the problem of consistency of risk measures with respect to usual stochastic
order and convex order. It is shown that under weak regularity conditions risk measures …

This paper studies the optimal reinsurance problem when risk is measured by a general risk
measure. Necessary and sufficient optimality conditions are given for a wide family of risk …

Subadditivity is the key property which distinguishes the popular risk measures Value-at-
Risk and Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of …

Risk measures have been studied for several decades in the actuarial literature, where they
appeared under the guise of premium calculation principles. Risk measures and properties …

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are
facing risk and uncertainty, though the classical uncertainty free case is also included. The …

According to the gradient allocation principle based on a positively homogeneous and
subadditive risk measure, the capital allocated to a sub-portfolio is the Gâteaux derivative …