We study the single particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.Comment: 11 pages, 11 figures, revtex

We investigate the localization properties of the single particle spectrum of a one-dimensional speckle potential in a box. We consider both the repulsive and the attractive cases. The system is controlled by two parameters: the size of the box and a rescaled potential intensity. The latter is a function of the particle mass, the correlation length and the average intensity of the field. Depending on both these parameters values and the considered energy level, the eigenstates exhibit different regimes of localization. In order to identify the regimes for the excited states, we use a technique developed in this work. Depending on the chosen parameters values, we find that it is possible not observing any effective mobility edge nor delocalization of the eigenstates due to the finite size of the system.Comment: 16 pages, 11 figure

The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.

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Public works contracts are commonly priced and awarded through a tender process. Each bidder joining the tender must underwrite a bid bond that guarantees their fitness as contractors in case of a win. The winning contractor also needs to underwrite a performance bond before entering the contract to protect the procuring entity against the performance risk arising during the execution phase. This study addresses the case when sureties refuse to issue the performance bond, despite having issued a bid bond to the same subject. A creditworthiness variation of the contractor during the tender or an excessive discount of the contract’s price may lead to this outcome. In that case, all the subjects involved are damaged. The surety who issued the bid bond has to indemnify the procuring entity. The contract award is nullified, which is financially harmful to both the contractor and the procuring entity. We show that sureties adopting a forward-looking risk appetite framework may prevent the demand for unsustainable performance bonds instead of addressing it by rejecting the bidders’ requests. The Solvency II regulatory framework, the Italian bidding law, and actual historical data available from the Italian construction sector are considered to specify a simplified model. The probability of unsustainable tender outcomes is numerically estimated by the model, together with the mitigating impact of a surety’s proper strategy.