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    Dynamic risk measures on variable exponent Bochner--Lebesgue spaces

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    In this paper, we will study several classes of risk measures on a special space Lp(â‹…)L^{p(\cdot)} where the variable exponent p(â‹…)p(\cdot) is no longer a given real number like the space LpL^{p}, but a random variable, which reflects the possible volatility of the financial markets. The dual representations for them are also provided

    On universal modular symbols

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    We clarify the relationship between works of Lee-Szczarba and Ash-Rudolph on the homology of the Steinberg module of a linear Tits building. This yields a simple proof of the Solomon-Tits theorem in this special case. We also give a (weak) relationship between this combinatorics and the one studied by van der Kallen, Suslin and Nesterenko to compute the homology of the general linear group with constant coefficients.Comment: 13
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