1,551 research outputs found
Capital allocation and bank management based on the quantification of credit risk
This paper was presented at the conference "Financial services at the crossroads: capital regulation in the twenty-first century" as part of session 2, "Credit risk modeling." The conference, held at the Federal Reserve Bank of New York on February 26-27, 1998, was designed to encourage a consensus between the public and private sectors on an agenda for capital regulation in the new century.Bank capital ; Bank loans ; Risk ; Bank management
Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with an Index-two saddle
Reactivity boundaries that divide the destination and the origin of
trajectories are of crucial importance to reveal the mechanism of reactions. We
investigate whether such reactivity boundaries can be extracted for higher
index saddles in terms of a nonlinear canonical transformation successful for
index-one saddles by using a model system with an index-two saddle. It is found
that the true reactivity boundaries do not coincide with those extracted by the
transformation taking into account a nonlinearity in the region of the saddle
even for small perturbations, and the discrepancy is more pronounced for the
less repulsive direction of the index-two saddle system. The present result
indicates an importance of the global properties of the phase space to identify
the reactivity boundaries, relevant to the question of what reactant and
product are in phase space, for saddles with index more than one
Reactivity Boundaries to Separate the Fate of a Chemical Reaction Associated with Multiple Saddles
Reactivity boundaries that divide the origin and destination of trajectories
are crucial of importance to reveal the mechanism of reactions, which was
recently found to exist robustly even at high energies for index-one saddles
[Phys. Rev. Lett. 105, 048304 (2010)]. Here we revisit the concept of the
reactivity boundary and propose a more general definition that can involve a
single reaction associated with a bottleneck made up of higher index saddles
and/or several saddle points with different indices, where the normal form
theory, based on expansion around a single stationary point, does not work. We
numerically demonstrate the reactivity boundary by using a reduced model system
of the cation where the proton exchange reaction takes place through a
bottleneck made up of two index-two saddle points and two index-one saddle
points. The cross section of the reactivity boundary in the reactant region of
the phase space reveals which initial conditions are effective in making the
reaction happen, and thus sheds light on the reaction mechanism.Comment: 12 pages, 7 figure
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