We model aggregate credit losses on large portfolios of financial positions contracted with firms subject to both cyclical default correlation and direct default contagion processes. Cyclical correlation is due to the dependence of firms on common (macro-) economic factors; credit contagion...

The paper provides an axiomatic characterization of dynamic risk measures for multi-period financial positions. For the special case of a terminal cash flow, we require that risk depends on its conditional distribution only. We prove a representation theorem for dynamic risk measures and...

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

We derive approximate formulae for the credit value-at-risk and the economic capital of a large credit portfolio. The representation allows to change the risk horizon quickly and avoids simulation or numerical procedures. The Poisson mixture model is equivalent to CreditRisk and uses the same...

Most credit portfolio models exclusively calculate the loss distribution for a portfolio of performing counterparts. Conservative default definitions cause considerable insecurity about the loss for a long time after the default. We present three approaches to account for defaulted counterparts...

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

Ende der 90er Jahre schien eine intensive Auswahl der Investments kaum notwendig, da fast jede Aktienanlage deutliche Kursgewinne versprach. Nach dem jähen Absturz an den Börsen haben die Anleger einen beträchtlichen Teil ihres Aktienvermögens verloren. Damit rücken wieder verstärkt...

The risk of a credit portfolio depends crucially on correlations between latent covariates, for instance the probability of default (PD) in different economic sectors. Often, correlations have to be estimated from relatively short time series, and the resulting estimation error hinders the...