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  • Electronic Resource  (3)
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  • 2000-2004  (3)
  • 2001  (3)
  • PACS. 02.50.Ey Stochastic processes – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 89.90.+n Other topics in areas of applied and interdisciplinary physics  (2)
  • AMS Classification. 65L05; 22E60.  (1)
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  • Electronic Resource  (3)
  • E-Resource
  • Loose Leaf
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  • 2000-2004  (3)
Year
  • 2001  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Empirical properties of the variety of a financial portfolio and the single-index model (2001)
    Springer
    The European physical journal 20 (2001), S. 503-509 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 02.50.Ey Stochastic processes – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 89.90.+n Other topics in areas of applied and interdisciplinary physics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We investigate the variety of a portfolio of stocks in normal and extreme days of market activity. We show that the variety carries information about the market activity which is not present in the single-index model and we observe that the variety time evolution is not time reversal around the crash days. We obtain the theoretical relation between the square variety and the mean return of the ensemble return distribution predicted by the single-index model. The single-index model is able to mimic the average behavior of the square variety but fails in describing quantitatively the relation between the square variety and the mean return of the ensemble distribution. The difference between empirical data and theoretical description is more pronounced for large positive values of the mean return of the ensemble distribution. Other significant deviations are also observed for extreme negative values of the mean return.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100510170229
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  • 2
    Electronic Resource
    Electronic Resource
    Langevin dynamics of financial systems: A second-order analysis (2001)
    Springer
    The European physical journal 22 (2001), S. 123-127 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 02.50.Ey Stochastic processes – 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion – 89.90.+n Other topics in areas of applied and interdisciplinary physics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat Cq, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that Cq can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00011127
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On Cayley-Transform Methods for the Discretization of Lie-Group Equations (2001)
    Springer
    Foundations of computational mathematics 1 (2001), S. 129-160 
    Details
    ISSN: 1615-3383
    Keywords: AMS Classification. 65L05; 22E60.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. In this paper we develop in a systematic manner the theory of time-stepping methods based on the Cayley transform. Such methods can be applied to discretize differential equations that evolve in some Lie groups, in particular in the orthogonal group and the symplectic group. Unlike many other Lie-group solvers, they do not require the evaluation of matrix exponentials. Similarly to the theory of Magnus expansions in [13], we identify terms in a Cayley expansion with rooted trees, which can be constructed recursively. Each such term is an integral over a polytope but all such integrals can be evaluated to high order by using special quadrature formulas similar to the construction in [13]. Truncated Cayley expansions (with exact integrals) need not be time-symmetric, hence the method does not display the usual advantages associated with time symmetry, e.g., even order of approximation. However, time symmetry (with its attendant benefits) is attained when exact integrals are replaced by certain quadrature formulas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s102080010003
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    Paper (German National Licenses)
    Fulltext
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