By Andras Kornai
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Additional resources for Mathematical And Statistical Methods In Insurance And Finance
Lai and M. , Amaral L. A. , Meyer M. and Stanley H. , Scaling of the distribution of fluctuations of financial market indices, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. , F. Seluuk and B. Whitcher, Scaling properties of foreign exchange volatility, Physica A 289, 249–266 (2001) 42 S. Bianchi and A. Pianese [GX03] [HUR51] [KL01] [LAM62] [LO91] [MAN63] [MEN04] [MDO90] [MDB00] [ONA04] [PBH94] [SSL00] [VA98] [YMH05] Genc¸ay R. , Scaling, self-similarity and multifractality in FX markets, Physica A, 323, 578–590 (2003) Hurst H.
The attention is then devoted to the study of the difference between risk measures of upper and lower bounds, with the aim of obtaining some information on random variables for which the gap is maximum or minimum. The paper is organized as follows. In Section 2, we first review some basic settings for describing the problem of measuring a risk and we recall some definitions and preliminary results in the field of distortion risk measures. We then propose the study of the case of a discrete risk with finitely many mass points in such a way that it is possible to give an explicit formula for its distortion risk measure.
Opposite evidence is provided for the volumes, characterized by (generally low) self-similarity parameters which are somewhat uniform with respect to the pairs of time horizons. Key words: Scaling; Self-similarity; Stock indexes. 1 Introduction Since the pioneering work by [MAN63], the scaling properties of financial returns have become the subject of a growing number of contributions for both theoretical and practical reasons. From a theoretical viewpoint, scaling invariance implies the absence of preferred investment time horizons and the consequent universality and parsimony of the model; practical advantages concern the possibility of building models stable under aggregation, analytically simple and governed by a small number of parameters.
Mathematical And Statistical Methods In Insurance And Finance by Andras Kornai