Coherent Risk Measures and Upper Previsions

In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (VaR), are studied from the perspective of the theory of coherent imprecise previsions. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. We also show that Value-at-Risk does not necessarily satisfy a weaker notion of coherence called ‘avoiding sure loss’ (ASL), and discuss both sufficient conditions for VaR to avoid sure loss and ways of modifying VaR into a coherent risk measure.Coherent risk measure, imprecise prevision, Value-at-Risk, avoiding sure loss condition

Constructing imprecise probabilities using arguments as evidence

This paper addresses the problem of constructing subjective imprecise probabilities using qualitative and conflicting pieces of information (arguments) as evidence.We propose formulae for the calculus of imprecise probabilities and show that the probabilities obtained reflect the indeterminacy of the subject, faithfully quantify the support offered by the arguments and constitute previsions that are mathematically coherent in the sense of [Walley, 1991]

Computational Determination of Coherence of Financial Risk Measure as a Lower Prevision of Imprecise Probability

This study is about developing some further ideas in imprecise probability models of financial risk measures. A financial risk measure has been interpreted as an upper prevision of imprecise probability, which through the conjugacy relationship can be seen as a lower prevision. The risk measures selected in the study are value-at-risk (VaR) and conditional value-at-risk (CVaR). The notion of coherence of risk measures is explained. Stocks that are traded in the financial markets (the risky assets) are seen as the gambles. The study makes a determination through computation from actual assets data whether the risk measure assessments of gambles (assets) are coherent as an imprecise probability. It is observed that coherence of assessments depends on the asset's returns distribution characteristic

Argumentation as a practical foundation for decision theory

Imperial Users onl

Coherent Risk Measures and Upper Previsions

In this paper coherent risk measures and other currently used risk measures, notably Value-at-Risk (V aR), are studied from the perspective of the theory of coherent imprecise previsions. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. We also show that Value-at-Risk does not necessarily satisfy a weaker notion of coherence called ‘avoiding sure loss ’ (ASL), and discuss both sufficient conditions for V aR to avoid sure loss and ways of modifying V aR into a coherent risk measure