Open AccessБулевозначный подход к анализу условного риска
Author(s) -
J.M. Zapata
Publication year - 2019
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.23671/vnc.2019.21.44629
Subject(s) - mathematics , risk measure , representation theorem , dynamic risk measure , coherent risk measure , duality (order theory) , measure (data warehouse) , dual representation , regular polygon , probability measure , dual (grammatical number) , representation (politics) , convex analysis , mathematical economics , discrete mathematics , computer science , convex optimization , economics , data mining , portfolio , art , geometry , literature , politics , political science , financial economics , law
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, aconditional risk measure can be interpreted as a classical convex risk measure within asuitable set-theoretic model. As a consequence, many properties of a conditional risk measure can be interpreted as basic properties of convex risk measures. This amounts to a method to interpret a theorem ofdual representation of convex risk measures as a new theorem of dual representation of conditional risk measures. As an instance of application, we establish a general robust representation theorem for conditional risk measures and study different particular cases of it.