216 research outputs found
Angular Gelfand--Tzetlin Coordinates for the Supergroup UOSp(k_1/2k_2)
We construct Gelfand--Tzetlin coordinates for the unitary orthosymplectic
supergroup UOSp(k_1/2k_2). This extends a previous construction for the unitary
supergroup U(k_1/k_2). We focus on the angular Gelfand--Tzetlin coordinates,
i.e. our coordinates stay in the space of the supergroup. We also present a
generalized Gelfand pattern for the supergroup UOSp(k_1/2k_2) and discuss
various implications for representation theory
An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices
We compute an analogue of the Itzykson-Zuber integral for the case of
arbitrary complex matrices. The calculation is done for both ordinary and
supermatrices by transferring the Itzykson-Zuber diffusion equation method to
the space of arbitrary complex matrices. The integral is of interest for
applications in Quantum Chromodynamics and the theory of two-dimensional
Quantum Gravity.Comment: 20 pages, RevTeX, no figures, agrees with published version,
including "Note added in proof" with an additional result for rectangular
supermatrice
Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations
We review recent progress in modeling credit risk for correlated assets. We
start from the Merton model which default events and losses are derived from
the asset values at maturity. To estimate the time development of the asset
values, the stock prices are used whose correlations have a strong impact on
the loss distribution, particularly on its tails. These correlations are
non-stationary which also influences the tails. We account for the asset
fluctuations by averaging over an ensemble of random matrices that models the
truly existing set of measured correlation matrices. As a most welcome side
effect, this approach drastically reduces the parameter dependence of the loss
distribution, allowing us to obtain very explicit results which show
quantitatively that the heavy tails prevail over diversification benefits even
for small correlations. We calibrate our random matrix model with market data
and show how it is capable of grasping different market situations.
Furthermore, we present numerical simulations for concurrent portfolio risks,
i.e., for the joint probability densities of losses for two portfolios. For the
convenience of the reader, we give an introduction to the Wishart random matrix
model.Comment: Review of a new random matrix approach to credit ris
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