[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/entropic-value-at-risk-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki24\/entropic-value-at-risk-wikipedia\/","headline":"Entropic value at risk – Wikipedia","name":"Entropic value at risk – Wikipedia","description":"In financial mathematics and stochastic optimization, the concept of risk measure is used to quantify the risk involved in a","datePublished":"2015-03-15","dateModified":"2015-03-15","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki24\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9d77104a5c3c49cc0634dcf6908db7ad45f738d2","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9d77104a5c3c49cc0634dcf6908db7ad45f738d2","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/en\/wiki24\/entropic-value-at-risk-wikipedia\/","wordCount":21571,"articleBody":"In 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,[1][2] 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. Because of its connection with the VaR and the relative entropy, this risk measure is called “entropic value at risk”. The EVaR was developed to tackle some computational inefficiencies[clarification needed] of the CVaR. Getting inspiration from the dual representation of the EVaR, Ahmadi-Javid[1][2] developed a wide class of coherent risk measures, called g-entropic risk measures. Both the CVaR and the EVaR are members of this class.Definition[edit]Let (\u03a9,F,P){displaystyle (Omega ,{mathcal {F}},P)} be a probability space with \u03a9{displaystyle Omega } a set of all simple events, F{displaystyle {mathcal {F}}} a \u03c3{displaystyle sigma }-algebra of subsets of \u03a9{displaystyle Omega } and P{displaystyle P} a probability measure on F{displaystyle {mathcal {F}}}. Let X{displaystyle X} be a random variable and LM+{displaystyle mathbf {L} _{M^{+}}} be the set of all Borel measurable functions X:\u03a9\u2192R{displaystyle X:Omega to mathbb {R} } whose moment-generating function MX(z){displaystyle M_{X}(z)} exists for all z\u22650{displaystyle zgeq 0}. The entropic value at risk (EVaR) of X\u2208LM+{displaystyle Xin mathbf {L} _{M^{+}}} with confidence level 1\u2212\u03b1{displaystyle 1-alpha } is defined as follows:"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/entropic-value-at-risk-wikipedia\/#breadcrumbitem","name":"Entropic value at risk – Wikipedia"}}]}]