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We propose two structural models for stochastic losses given default which allow to model the credit losses of a portfolio of defaultable financial instruments. The credit losses are integrated into a structural model of default events…
We discuss the role of integrated chance constraints (ICC) as quantitative risk constraints in asset and liability management (ALM) for pension funds. We define two types of ICC: the one period integrated chance constraint (OICC) and the…
We study cross-country GDP losses due to financial crises in terms of frequency (number of loss events per period) and severity (loss per occurrence). We perform the Loss Distribution Approach (LDA) to estimate a multi-country aggregate GDP…
Regulation and risk management in banks depend on underlying risk measures. In general this is the only purpose that is seen for risk measures. In this paper we suggest that the reporting of risk measures can be used to determine the loss…
The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
This paper introduces a relative model risk measure of a product priced with a given model, with respect to another reference model for which the market is assumed to be driven. This measure allows comparing products valued with different…
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…
The downside risk of a portfolio of (equity)assets is generally substantially higher than the downside risk of its components. In particular in times of crises when assets tend to have high correlation, the understanding of this difference…
This paper develops a structural credit risk model to characterize the difference between the economic and recorded default times for a firm. Recorded default occurs when default is recorded in the legal system. The economic default time is…
According to the Loss Distribution Approach, the operational risk of a bank is determined as 99.9% quantile of the respective loss distribution, covering unexpected severe events. The 99.9% quantile can be considered a tail event. As…
The framework of this paper is that of risk measuring under uncertainty, which is when no reference probability measure is given. To every regular convex risk measure on ${\cal C}_b(\Omega)$, we associate a unique equivalence class of…
In this article we use the Mean-Variance Model in order to measure the current market state. In our study we take the approach of detecting the overall alignment of portfolios in the spin picture. The projection to the ground-states enables…
Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely…
The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as…
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that…
We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be…
In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between…
The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios…
We test the hypothesis that interconnections across financial institutions can be explained by a diversification motive. This idea stems from the empirical evidence of the existence of long-term exposures that cannot be explained by a…