This paper characterizes performance measures satisfying a set of proposed axioms. We develop four new measures consistent with the axioms and show that they improve on the economic properties of the Sharpe Ratio and the Gain-Loss Ratio. In our treatment, the performance measures, or the indices...

The paper has 2 main goals:1. We propose a variant of the CAPM based on coherent risk.2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure provides a powerful tool for investigating the relation...

We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected...

We propose a new procedure for the risk measurement of large portfolios.It employs the following objects as the building blocks:- coherent risk measures introduced by Artzner, Delbaen, Eber, and Heath;- factor risk measures introduced in this paper, which assess the risks driven by particular...

This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered. Furthermore, the results obtained are applied to the...

This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a...

Hedge fund returns have scarce observations, and from the data one can successfully estimate the joint laws of the return with each of risk driving factors but cannot estimate higher-dimensional joint laws. We propose a methodology to recover from this information the conditional mean of the...

We investigate a class of concave monetary utility functions, which we call divergence utilities. Divergence utilities are the translation invariant hull of expected utilities. This class is rather wide and includes, in particular, the entropic utility. More important, this class is very...

We consider the problem of measuring the risk of a portfolio with scarce observations by linking it to several risk factors. A typical example is measuring the risk of a hedge fund. It is assumed that from the available data one can estimate the joint law of all the factors as well as all the...