By Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi
A likelihood Metrics method of monetary possibility Measures relates the sector of chance metrics and chance measures to each other and applies them to finance for the 1st time.
- Helps to reply to the query: which danger degree is healthier for a given problem?
- Finds new family members among latest sessions of probability measures
- Describes functions in finance and extends them the place possible
- Presents the speculation of likelihood metrics in a extra available shape which might be applicable for non-specialists within the field
- Applications contain optimum portfolio selection, threat idea, and numerical tools in finance
- Topics requiring extra mathematical rigor and element are integrated in technical appendices to chapters
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Additional resources for A Probability Metrics Approach to Financial Risk Measures
In this chapter, we briefly describe expected utility theory and the stochastic dominance relations that result. We apply the stochastic dominance relations to the portfolio choice problem and check how the theory of probability metrics can be combined with the stochastic dominance relations. 2 Expected Utility Theory We start with the well-known St Petersburg Paradox, which is historically the first application of the concept of the expected utility function. As a next step, we describe the essential result of von Neumann–Morgenstern characterization of the preferences of individuals.
Kaufman, R. (1984), ‘Fourier transforms and descriptive set theory’, Mathematika 31, 336–339. Kruglov, V. M. (1973), ‘Convergence of numerical characteristics of independent random variables with values in a Hilbert space’, Theory Prob. Appl. 18, 694–712. Kuratowski, K. (1969), Topology, Vol. II, Academic, New York. Lebesgue, H. (1905), ‘Sur les fonctions representables analytiquement’, J. Math. Pures Appl. V, 139–216. Loeve, M. (1963), Probability Theory, 3rd edn, Van Nostrand, Princeton. Lukacs, E.
Let (S, ) be a metric space, and let (C(S), r) be the space described above. If (S, ) is separable [resp. complete; resp. totally bounded], then (C(S), r) is separable [resp. complete; resp. totally bounded]. Proof. See Hausdorff (1949), section 29, and Kuratowski (1969), sections 21 and 23. 4. Let S = [0, 1] and let be the usual metric on S. Let R be the set of all finite complex-valued Borel measures m on S such that the Fourier transform m(t) = 1 exp(iut)m(du) 0 vanishes at t = ±∞. Let M be the class of sets E ∈ C(S) such that there is some m ∈ R concentrated on E.