The concept of coherent risk measure was introduced in Artzner et al. (1999). They listed some properties, called axioms of ‘coherence’, that any good risk measure should possess, and studied the (non-)coherence of widely-used risk measure such as Value-atRisk (VaR) and expected shortfall (also known as tail conditional expectation or tail VaR). Kusuoka (2001) introduced two additional axioms c...

The theory of copulae is known to provide a useful tool for modelling dependence in integrated risk management. In the present paper we review and extend some of the more recent results for finding distributional bounds for functions of dependent risks. As an example, the main emphasis is put on Value-at-Risk as a risk measure.

We introduce a generalised subgradient for law-invariant closed convex risk measures on L and establish its relationship with optimal risk allocations and equilibria. Our main result gives sufficient conditions ensuring a non-empty generalised subgradient.

A common problem is to choose a “risk neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X , together with the behavior of the option prices for a relevant famil...

— This paper defends the wisdom of not considering the Digital Economy to be one homogeneous sector. Our hypothesis is that it is best to consider it the result of adding four different subsectors. We test whether indeed the economic and financial performance of a portfolio of listed companies in each of the four subsectors presents relevant differences. We use the value at risk measure to esti...

For decades, performance comparisons between real estate and financial assets have repeatedly indicated that private real estate investment exhibits significantly higher risk-adjusted returns than publicly traded financial assets such as common stocks. That is, there is an apparent “real estate risk premium puzzle.” In this paper, we find that the seemingly superior risk-adjusted returns of rea...

The authors present an alternative representation of risk measures originally defined in terms of expectations with respect to distorted probabilities. They also show that the right-tail, left-tail, and two-sided deviations/indices suggested by Wang (1998) can be represented in this alternative form. Empirical estimators for these quantities are proposed and their properties explored.

This paper identifies the macroeconomic factors that influence Italian equity returns and tests the stability of their relation with securities returns. In the sixteen-year period that has been analyzed the relation between stock returns and the macroeconomic factors is found to be highly unstable: not only are the betas of individual securities virtually uncorrelated over time, but a high perc...

We develop a methodology to optimally design a financial issue to hedge non-tradable risk on financial markets.The modeling involves a minimization of the risk borne by issuer given the constraint imposed by a buyer who enters the transaction if and only if her risk level remains below a given threshold. Both agents have also the opportunity to invest all their residual wealth on financial mark...