[PDF] Top 20 A Representation of Risk Measures

... every risk measure satisfying (1), (2) and (3) corresponds to an integration over a set measures, but integration is in the sense of ...is a measure, integration is Lebesgue integration ... Voir le document complet

... market risk - since 1995 (BCBS for instance) - that "the VaR risk measure is inadequate for measuring the risks because it does not take into account the extreme events" and also "one of ... Voir le document complet

... BSDEs of first type, they rely on the special case F (t, X) = E[ϕ(t, ...in a hypothetical large scale ...dynamic risk measures induced by the mean-field ...intensity of network ... Voir le document complet

... tion of law invariant coherent risk measures, satisfying the Fatou prop- ...notion of coherent risk measures to the more general notion of convex risk ... Voir le document complet

... Coherent risk measures for finite probability spaces were introduced in [5] and were extended to general probability spaces in [33], where applications to risk measurement, premium calculation and ... Voir le document complet

... to a life insurer since lapses aect pric- ing, reserving, protability, liquidity, risk management, as well as the solvency of the ...Lapse risk is indeed the most signicant life ... Voir le document complet

... the risk managers to compute the spectrum to have a better understanding of these ...terms of risks, the first point to consider, as we have seen previously, is to fit a ... Voir le document complet

... control of lighting and heating, aiming to increase energy efficiency and comfort of the ...surveillance of buildings [1]. It is attempted to monitor what is going in a building without the ... Voir le document complet

... at Risk of a position X , VaR α (X ) = −in f {x : P(X > x) ≤ 1 − α } Since the 1951 paper of Markowitz, many have also favored the usefulness of ...and a simple example shows ... Voir le document complet

... evaluate risk as a linear function of the actual probabilities for different outcomes but rather as a non-linear distortion ...probabilities of the loss distribution to another ... Voir le document complet

... authorize a wider selection of the marginal distributions of the financial ...allow a less banal representation of the statistical dependence in finance based on the traditional ... Voir le document complet

... properties of dynamic risk measures induced by BSDEs with ...case of a concave driver f, we provide a dual representation prop- erty of the associated convex ... Voir le document complet

... at Risk of a position X , VaR α (X ) = −in f {x : P(X > x) ≤ 1 − α } Since the 1951 paper of Markowitz, many have also favored the usefulness of ...and a simple example shows ... Voir le document complet

... Abstract: Risk management is currently shifting from the full protection against flooding towards the management of the consequences of ...modelling of the inundation flow, nearby land use and ... Voir le document complet

... loss-based risk measures and provides a representation theorem in terms of a penalty function (Theorem 1), which adapts the results of F¨ollmer and Schied (2004) to our ... Voir le document complet

... formalization of mathematics, algebraic numbers, frac- tions, polynomials, Newton power series ...as a basis for computations. For example, a real algebraic number is represented by a nonzero ... Voir le document complet

... Dictionary of Economics, Gilles Duranton wrote “On the empirical front, a first key challenge is to develop new tools for spatial ...Measurement of the spatial concentration of activities is ... Voir le document complet

... condition, a collective absence of arbitrage condition, which requires that investors do not engage in mutually compatible, utility nondecreasing ...existence of equilibrium (see ...For a ... Voir le document complet

... for a subclass of risk measures and called it the Pareto equilibrium ...non-emptyness of the intersection of the relative interiors of agents’ sets of priors (see ... Voir le document complet

... problem of the existence and characterization of Pareto optima and equi- libria in markets with short-selling, an old problem in the economic literature, has recently been addressed by Barrieu and El Karoui ... Voir le document complet