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  • 2000-2004  (4)
  • 2001  (4)
  • PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes  (2)
  • PACS. 75.10.Nr Spin-glass and other random models  (2)
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  • 2000-2004  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    The Bethe lattice spin glass revisited (2001)
    Springer
    The European physical journal 20 (2001), S. 217-233 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 75.10.Nr Spin-glass and other random models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00011099
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Beliefs and stochastic modelling of interest rate scenario risk (2001)
    Springer
    The European physical journal 20 (2001), S. 511-515 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We present a framework that allows for a systematic assessment of risk given a specific model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which allows for a (time-)local understanding of its level, together with a short term forecast. On the other hand, via a diffusion approximation, the time evolution of the probability density of risk is modeled by a Fokker-Planck equation. Then, as a final step, using Bayes theorem, beliefs are conditioned on the stationary probability density function as obtained from the Fokker-Planck equation. We believe this to be a highly rigorous framework to integrate subjective judgments of future market behavior and underlying models. In order to demonstrate the approach, we apply it to risk assessment of empirical interest rate scenario methodologies, i.e. the application of Principal Component Analysis to the the dynamics of bonds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00011107
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Extracting factors for interest rate scenarios (2001)
    Springer
    The European physical journal 20 (2001), S. 517-522 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Tp Time series analysis – 02.50.Ey Stochastic processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Factor based interest rate models are widely used for risk managing purposes, for option pricing and for identifying and capturing yield curve anomalies. The movements of a term structure of interest rates are commonly assumed to be driven by a small number of orthogonal factors such as SHIFT, TWIST and BUTTERFLY (BOW). These factors are usually obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). Although PCA diagonalizes the covariance matrix of either the interest rates or the interest rate changes, it does not use both covariance matrices simultaneously. Furthermore higher linear and nonlinear correlations are neglected. These correlations as well as the mean reverting properties of the interest rates become crucial, if one is interested in a longer time horizon (infrequent hedging or trading). We will show that Independent Component Analysis (ICA) is a more appropriate tool than PCA, since ICA uses the covariance matrix of the interest rates as well as the covariance matrix of the interest rate changes simultaneously. Additionally higher linear and nonlinear correlations may be easily incorporated. The resulting factors are uncorrelated for various time delays, approximately independent but nonorthogonal. This is in contrast to the factors obtained from the PCA, which are orthogonal and uncorrelated for identical times only. Although factors from the ICA are nonorthogonal, it is sufficient to consider only a few factors in order to explain most of the variation in the original data. Finally we will present examples that ICA based hedges outperforms PCA based hedges specifically if the portfolio is sensitive to structural changes of the yield curve.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    The ± J spin glass in Migdal-Kadanoff approximation (2001)
    Springer
    The European physical journal 21 (2001), S. 589-594 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 75.10.Nr Spin-glass and other random models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We study the low-temperature phase of the three-dimensional ± J Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T 〉 0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to T -2/ds where ds is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100510170169
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    Paper (German National Licenses)
    Fulltext
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