This paper introduces a set of axioms that define convex risk measures. Duality theory provides the representation theorem for these measures and the link with pricing rules. 2002 Published by Elsevier Science B.V. JEL classification: G11; G12; G13

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...

Institute of Computational Modeling SB RAS, Academgorodok, Krasnoyarsk, Russia, 660036 e-mail: [email protected], phone +7 3912 495382 Abstract Risk measures are widely used in insurance pricing, portfolio selection, and in decision-making in general. Two prevalent classes of risk measures are expected utility (a dollar transform), and distorted probability (a probability transform). Both appro...

Our society is fascinated with risk in many different areas and disciplines. One of the main ways to describe and communicate the level of risk is through risk indices, which summarize risk using numbers or categories such as words, letters, or colors. These indices are used to communicate risks to the public, understand how risk is changing over time, compare among different risks, and support...

This paper presents an optimal portfolio selection approach based on value at risk (VaR), conditional value at risk (CVaR), worst-case value at risk (WVaR) and partitioned value at risk (PVaR) measures as well as calculating these risk measures. Mathematical solution methods for solving these optimization problems are inadequate and very complex for a portfolio with high number of assets. For t...

Artzner, Delbaen, Eber and Heath ([1]) initialized a new direction to assess risks of financial positions by an axiomatic approach. It relies fundamentally on the concept of risk measures, which are functionals on sets of financial positions satisfying some basic properties. The convex risk measures are exactly those ones which guarantee that diversification does not increase the risk. From the...

Background & Aims of the Study: Identification of hazards is one of the first goals of risk analysis. Failure mode and effect analysis method (FMEA) is universally defined as efficient procedures for finding potential failures aimed to remove or decrease the risk which is related to them. This study aimed to investigate the effect of control measures on reduction of risk ev...