RisqueLe risque est la possibilité de survenue d'un événement indésirable, la probabilité d’occurrence d'un péril probable ou d'un aléa. Le risque est une notion complexe, de définitions multiples car d'usage multidisciplinaire. Néanmoins, il est un concept très usité depuis le , par exemple sous la forme de l'expression , notamment pour qualifier, dans le sens commun, un événement, un inconvénient qu'il est raisonnable de prévenir ou de redouter l'éventualité.
Risque financierUn risque financier est un risque de perdre de l'argent à la suite d'une opération financière (sur un actif financier) ou à une opération économique ayant une incidence financière (par exemple une vente à crédit ou en devises étrangères). Le risque de marché est le risque de perte qui peut résulter des fluctuations des prix des instruments financiers qui composent un portefeuille. Le risque de contrepartie est le risque que la partie avec laquelle un contrat a été conclu ne tienne pas ses engagements (livraison, paiement, remboursement, etc.
Expected shortfallExpected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL), and superquantile.
Risk measureIn financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator. In recent years attention has turned towards convex and coherent risk measurement. A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns.
Coherent risk measureIn the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk measure is a function that satisfies properties of monotonicity, sub-additivity, homogeneity, and translational invariance. Consider a random outcome viewed as an element of a linear space of measurable functions, defined on an appropriate probability space.
Gestion des risquesLa gestion des risques, ou l'anglicisme, management du risque (de l'risk management), est la discipline visant à identifier, évaluer et hiérarchiser les risques liés aux activités d'une organisation, quelles que soient la nature ou l'origine de ces risques, puis à les traiter méthodiquement, de manière coordonnée et économique, afin de réduire et contrôler la probabilité des événements redoutés, et leur impact éventuel.
Risk aversionIn economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a more predictable, but possibly lower payoff, rather than another situation with a highly unpredictable, but possibly higher payoff.
Entropic value at riskIn financial mathematics and stochastic optimization, the concept of risk measure is used to quantify the risk involved in a random outcome or risk position. Many risk measures have hitherto been proposed, each having certain characteristics. The entropic value at risk (EVaR) is a coherent risk measure introduced by Ahmadi-Javid, which is an upper bound for the value at risk (VaR) and the conditional value at risk (CVaR), obtained from the Chernoff inequality. The EVaR can also be represented by using the concept of relative entropy.
Spectral risk measureA Spectral risk measure is a risk measure given as a weighted average of outcomes where bad outcomes are, typically, included with larger weights. A spectral risk measure is a function of portfolio returns and outputs the amount of the numeraire (typically a currency) to be kept in reserve. A spectral risk measure is always a coherent risk measure, but the converse does not always hold. An advantage of spectral measures is the way in which they can be related to risk aversion, and particularly to a utility function, through the weights given to the possible portfolio returns.
Value at riskLa VaR (de l'anglais value at risk, mot à mot : « valeur à risque », ou « valeur en jeu ») est une notion utilisée généralement pour mesurer le risque de marché d'un portefeuille d'instruments financiers. Elle correspond au montant de pertes qui ne devrait être dépassé qu'avec une probabilité donnée sur un horizon temporel donné. L'utilisation de la VaR n'est désormais plus limitée aux instruments financiers : on peut en faire un outil de gestion des risques dans tous les domaines (, par exemple).
Portfolio optimizationPortfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk. Factors being considered may range from tangible (such as assets, liabilities, earnings or other fundamentals) to intangible (such as selective divestment). Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz; see Markowitz model.
Théorie moderne du portefeuilleLa théorie moderne du portefeuille est une théorie financière développée en 1952 par Harry Markowitz. Elle expose comment des investisseurs rationnels utilisent la diversification afin d'optimiser leur portefeuille, et quel devrait être le prix d'un actif étant donné son risque par rapport au risque moyen du marché. Cette théorie fait appel aux concepts de frontière efficiente, coefficient bêta, droite de marché des capitaux et droite de marché des titres. Sa formalisation la plus accomplie est le modèle d'évaluation des actifs financiers ou MEDAF.
Portefeuille (finance)Un portefeuille (en finance) désigne une collection d'actifs financiers détenus par un établissement ou un individu. Cela peut aussi désigner des valeurs mobilières détenues à titre d'investissements, de dépôt, de provision ou de garantie. Une caractéristique importante d'un portefeuille est son degré de diversification qui permet d'atteindre un juste milieu entre le risque, la volatilité et la rentabilité du portefeuille, tout en tenant compte de la durée prévue du placement (horizon de temps).
Risque de changeLe risque de change d'un actif financier est le risque pesant sur une position concernant une devise par rapport à une autre au sujet de la variation future du cours de change. Par exemple, le fait de se faire payer en Europe, à terme, en dollars, peut, selon le cours euro-dollar, faire évoluer la valeur de la créance éventuellement accordée à un client américain. Le risque de change est un élément négatif du patrimoine de l'entreprise qui doit être valorisé en comptabilité.
Intertemporal portfolio choiceIntertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion. The set of asset proportions at any time defines a portfolio. Since the returns on almost all assets are not fully predictable, the criterion has to take financial risk into account. Typically the criterion is the expected value of some concave function of the value of the portfolio after a certain number of time periods—that is, the expected utility of final wealth.
Coherent sheafIn mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an , and so they are closed under operations such as taking , , and cokernels.
Financial risk modelingFinancial risk modeling is the use of formal mathematical and econometric techniques to measure, monitor and control the market risk, credit risk, and operational risk on a firm's balance sheet, on a bank's trading book, or re a fund manager's portfolio value; see Financial risk management. Risk modeling is one of many subtasks within the broader area of financial modeling. Risk modeling uses a variety of techniques including market risk, value at risk (VaR), historical simulation (HS), or extreme value theory (EVT) in order to analyze a portfolio and make forecasts of the likely losses that would be incurred for a variety of risks.
Financial risk managementFinancial risk management is the practice of protecting economic value in a firm by managing exposure to financial risk - principally operational risk, credit risk and market risk, with more specific variants as listed aside. As for risk management more generally, financial risk management requires identifying the sources of risk, measuring these, and crafting plans to address them. See for an overview. Financial risk management as a "science" can be said to have been born with modern portfolio theory, particularly as initiated by Professor Harry Markowitz in 1952 with his article, "Portfolio Selection"; see .
Finitely generated moduleIn mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
Faisceau (de modules)En mathématique, un faisceau de modules est un faisceau sur un espace localement annelé qui possède une structure de module sur le faisceau structural . Sur un espace localement annelé , un faisceau de -modules (ou un -Module) est un faisceau sur tel que soit un -module pour tout ouvert , et que pour tout ouvert contenu dans , l'application restriction soit compatible avec les structures de modules: pour tous , on a Les notions de sous--modules et de morphismes de -modules sont claires.
