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Institute
Banks increasingly recognize the need to measure and manage the credit risk of their loans on a portfolio basis. We address the subportfolio "middle market". Due to their specific lending policy for this market segment it is an important task for banks to systematically identify regional and industrial credit concentrations and reduce the detected concentrations through diversification. In recent years, the development of markets for credit securitization and credit derivatives has provided new credit risk management tools. However, in the addressed market segment adverse selection and moral hazard problems are quite severe. A potential successful application of credit securitization and credit derivatives for managing credit risk of middle market commercial loan portfolios depends on the development of incentive-compatible structures which solve or at least mitigate the adverse selection and moral hazard problems. In this paper we identify a number of general requirements and describe two possible solution concepts.
Ein Value-at-Risk-Limit wird als DM-Betrag gekennzeichnet, der von den tatsächlichen Handelsverlusten innerhalb einer bestimmten Zeitdauer nur mit geringer Wahrscheinlichkeit überschritten werden darf. Da der Bankvorstand i.d.R. Jahres-Value-at-Risk-Limite beschließt, im Handelsbereich die Geschäfte aber für einen kurzfristigen - unterstellt wird ein eintägiger - Planungshorizont abgeschlossen werden, ist zu klären, wie Jahres-Limite in Tages-Limite umgerechnet und während des Jahres realisierte Gewinne und Verluste auf die Limite angerechnet werden können. Auf der Grundlage des Umrechnungsverfahrens nach der Quadratwurzel-T-Formel lassen sich drei Verfahren für die Ermittlung des Tages-Limits unterscheiden: 1. Realisierte Gewinne und Verluste werden nicht angerechnet (starres Limit). 2. Bei Verlusteintritt vermindert sich das Tages-Limit für die Restperiode, realisierte Gewinne machen Kürzungen rückgängig (Verlustbegrenzungslimit). 3. Tages-Limite werden um Gewinne und Verluste angepaßt, wodurch eine Erweiterung des Handlungsspielraumes möglich ist (dynamisches Limit). Die drei Limite werden in einem Simulationsmodell gegeneinander abgewogen, wobei unterstellt wird, ein Händler handle nur eine einzige Aktie und antizipiere in 55% der Fälle die Kursrichtung. Die Simulationsergebnisse sind bei den unterstellten Renditeprozessen (geometrische Brownsche Bewegung und reale Renditen von 77 deutschen Aktien für die Zeit vom 01.01.1974 bis 31.12.1995) weitgehend identisch. Das dynamische Limit produziert deutlich höhere durchschnittliche Ergebnisse als das starre Limit und das Verlustbegrenzungslimit. Überschreitungen des Jahres-Limits treten nur beim starren Verfahren auf, die Häufigkeit ist allerdings wesentlich geringer als die zulässige Wahrscheinlichkeit von 1 %.
We present the first measurement of event-by-event fluctuations in the kaon sector in Pb – Pb collisions at √sNN = 2.76 TeV with the ALICE detector at the LHC. The robust fluctuation correlator νdyn is used to evaluate the magnitude of fluctuations of the relative yields of neutral and charged kaons, as well as the relative yields of charged kaons, as a function of collision centrality and selected kinematic ranges. While the correlator νdyn[K+,K−] exhibits a scaling approximately in inverse proportion of the charged particle multiplicity, νdyn[K0 S ,K±] features a significant deviation from such scaling. Within uncertainties, the value of νdyn[K0 S ,K±] is independent of the selected transverse momentum interval, while it exhibits a pseudorapidity dependence. The results are compared with HIJING, AMPT and EPOS–LHC predictions, and are further discussed in the context of the possible production of disoriented chiral condensates in central Pb – Pb collisions.
A measurement of the transverse momentum spectra of jets in Pb-Pb collisions at sNN−−−√=2.76 TeV is reported. Jets are reconstructed from charged particles using the anti-kT jet algorithm with jet resolution parameters R of 0.2 and 0.3 in pseudo-rapidity |η|<0.5. The transverse momentum pT of charged particles is measured down to 0.15 GeV/c which gives access to the low pT fragments of the jet. Jets found in heavy-ion collisions are corrected event-by-event for average background density and on an inclusive basis (via unfolding) for residual background fluctuations and detector effects. A strong suppression of jet production in central events with respect to peripheral events is observed. The suppression is found to be similar to the suppression of charged hadrons, which suggests that substantial energy is radiated at angles larger than the jet resolution parameter R=0.3 considered in the analysis. The fragmentation bias introduced by selecting jets with a high pT leading particle, which rejects jets with a soft fragmentation pattern, has a similar effect on the jet yield for central and peripheral events. The ratio of jet spectra with R=0.2 and R=0.3 is found to be similar in Pb-Pb and simulated PYTHIA pp events, indicating no strong broadening of the radial jet structure in the reconstructed jets with R<0.3.
In particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD)1. These partons subsequently emit further partons in a process that can be described as a parton shower2, which culminates in the formation of detectable hadrons. Studying the pattern of the parton shower is one of the key experimental tools for testing QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass mQ and energy E, within a cone of angular size mQ/E around the emitter3. Previously, a direct observation of the dead-cone effect in QCD had not been possible, owing to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible hadrons. We report the direct observation of the QCD dead cone by using new iterative declustering techniques4,5 to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD. Furthermore, the measurement of a dead-cone angle constitutes a direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics.
The production of J/ψ is measured as a function of charged-particle multiplicity at forward rapidity in proton-proton (pp) collisions at center-of-mass energies s√ = 5.02 and 13 TeV. The J/ψ mesons are reconstructed via their decay into dimuons in the rapidity interval (2.5 < y < 4.0), whereas the charged-particle multiplicity density (dNch/dη) is measured at midrapidity (|η| < 1). The production rate as a function of multiplicity is reported as the ratio of the yield in a given multiplicity interval to the multiplicity-integrated one. This observable shows a linear increase with charged-particle multiplicity normalized to the corresponding average value for inelastic events (dNch/dη/〈dNch/dη〉), at both the colliding energies. Measurements are compared with available ALICE results at midrapidity and theoretical model calculations. First measurement of the mean transverse momentum (〈pT〉) of J/ψ in pp collisions exhibits an increasing trend as a function of dNch/dη/〈dNch/dη〉 showing a saturation towards high charged-particle multiplicities.
We present a study of the inclusive charged-particle transverse momentum (pT) spectra as a function of charged-particle multiplicity density at mid-pseudorapidity, dNch/dη, in pp collisions at s√=5.02 and 13 TeV covering the kinematic range |η|<0.8 and 0.15<pT<20 GeV/c. The results are presented for events with at least one charged particle in |η|<1 (INEL>0). The pT spectra are reported for two multiplicity estimators covering different pseudorapidity regions. The pT spectra normalized to that for INEL>0 show little energy dependence. Moreover, the high-pT yields of charged particles increase faster than the charged-particle multiplicity density. The average pT as a function of multiplicity and transverse spherocity is reported for pp collisions at s√=13 TeV. For low- (high-) spherocity events, corresponding to jet-like (isotropic) events, the average pT is higher (smaller) than that measured in INEL>0 pp collisions. Within uncertainties, the functional form of ⟨pT⟩(Nch) is not affected by the spherocity selection. While EPOS LHC gives a good description of many features of data, PYTHIA overestimates the average pT in jet-like events.
J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at √sNN = 8.16 TeV
(2020)
Inclusive J/ψ yields and average transverse momenta in p-Pb collisions at a center-of-mass energy per nucleon pair s NN $$ \sqrt{s_{\mathrm{NN}}} $$ = 8.16 TeV are measured as a function of the charged-particle pseudorapidity density with ALICE. The J/ψ mesons are reconstructed at forward (2.03 < y cms < 3.53) and backward (−4.46 < y cms < −2.96) center-of-mass rapidity in their dimuon decay channel while the charged-particle pseudorapidity density is measured around midrapidity. The J/ψ yields at forward and backward rapidity normalized to their respective average values increase with the normalized charged-particle pseudorapidity density, the former showing a weaker increase than the latter. The normalized average transverse momenta at forward and backward rapidity manifest a steady increase from low to high charged-particle pseudorapidity density with a saturation beyond the average value.
The multiplicity dependence of jet production in pp collisions at the centre-of-mass energy of s√=13 TeV is studied for the first time. Jets are reconstructed from charged particles using the anti-kT algorithm with resolution parameters R varying from 0.2 to 0.7. The jets are measured in the pseudorapidity range |ηjet|<0.9−R and in the transverse momentum range 5<pchT,jet<140 GeV/c. The multiplicity intervals are categorised by the ALICE forward detector V0. The pT differential cross section of charged-particle jets are compared to leading order (LO) and next-to-leading order (NLO) perturbative quantum chromodynamics (pQCD) calculations. It is found that the data are better described by the NLO calculation, although the NLO prediction overestimates the jet cross section below 20 GeV/c. The cross section ratios for different R are also measured and compared to model calculations. These measurements provide insights into the angular dependence of jet fragmentation. The jet yield increases with increasing self-normalised charged-particle multiplicity. This increase shows only a weak dependence on jet transverse momentum and resolution parameter at the highest multiplicity. While such behaviour is qualitatively described by the present version of PYTHIA, quantitative description may require implementing new mechanisms for multi-particle production in hadronic collisions.
The energy deposited at very forward rapidities (very forward energy) is a powerful tool for characterising proton fragmentation in pp and p-Pb collisions. The correlation of very forward energy with particle production at midrapidity provides direct insights into the initial stages and the subsequent evolution of the collision. Furthermore, the correlation with the production of particles with large transverse momenta at midrapidity provides information complementary to the measurements of the underlying event, which are usually interpreted in the framework of models implementing centrality-dependent multiple parton interactions.
Results about very forward energy, measured by the ALICE zero degree calorimeters (ZDCs), and its dependence on the activity measured at midrapidity in pp collisions at s√ = 13 TeV and in p-Pb collisions at sNN−−−√ = 8.16 TeV are discussed. The measurements performed in pp collisions are compared with the expectations of three hadronic interaction event generators: PYTHIA 6 (Perugia 2011 tune), PYTHIA 8 (Monash tune), and EPOS LHC. These results provide new constraints on the validity of models in describing the beam remnants at very forward rapidities, where perturbative QCD cannot be used.