The work presents a novel method for the detection of mutual
phase synchronization in non-stationary time series. We show how the
application of a cluster algorithmthat considers spatio-temporal struc-
tures of data follows from the general condition of phase-synchronized
data. In view of the topology of phasic data, we re-formulate the
K-Means cluster algorithm on a flat torus and apply a segmentation
index derived in an earlier work (Physica D 177,203-232(2003)). This index is extended by means of averaging in order to reflect phase syn-
chronization in ensembles of multivariate time series. The method is
illustrated using simulated multivariate phase dynamics and arrays of
chaotic systems, in which temporal segments of phase-synchronized
states are registered. A comparison with results from an existing bi-
variate synchronization index reveals major advantages of our method.
Let Ex be a collection of i.i.d. exponential random
variables. Symmetric Bouchaud’s model on Z2 is a Markov chain
X(t) whose transition rates are given by wxy = ν exp(−βEx ) if x,
y are neighbours in Z2 . We study the behaviour of two correlation functions: P[X(tw + t) = X(tw )] and P X(t ) = X(tw )∀t ∈
[tw , tw + t] . We prove the (sub)aging behaviour of these functions
when β > 1.
We study perturbations of a stochastic program with a probabilistic constraint and r-concave original probability distribution. First we improve our earlier results substantially and provide conditions implying Hölder continuity properties of the solution sets w.r.t. the Kolmogorov distance of probability distributions. Secondly, we derive an upper Lipschitz continuity property for solution sets under more restrictive conditions on the original program and on the perturbed probability measures. The latter analysis applies to linear-quadratic models and is based on work by Bonnans and Shapiro. The stability results are illustrated by numerical tests showing the different asymptotic behaviour of parametric and nonparametric estimates in a program with a normal probabilistic constraint.
A popular model to describe credit risk in practice is CreditRisk
+
and in
this paper a Fourier inversion to obtain the distribution of the credit loss is
proposed. A deeper analysis of the Fourier transformation showed that there
are at least two methods to obtain the distribution although the corresponding
characteristic function is not integrable.
The CreditRisk
+
model will be extended such, that general dependent sec-
tor variables can be taken into consideration, for example dependent lognormal
sector variables. Then the transfer to a continuous time model will be per-
formed and the sector variables become processes, more precisely geometric
Brownian motions.
To have a time continuous credit risk model is an important step to combine
this model with market risk. Additionally a portfolio model will be presented
where the changes of the spreads are driven by the sector variables. Using a
linear expansion of the market risk, the distribution of this portfolio can be
determined. In the special case that there is no credit risk, this model yields
the well known Delta normal approach for market risk, hence a link between
credit risk and market risk has been established.
The CreditRisk model launched by CSFB in 1997 is widely used by practitioners in the banking sector as a simple means for the quantification of credit
risk, primarily of the loan book. We present an alternative numerical recursion scheme for CreditRisk, equivalent to an algorithm recently proposed by
Giese, based on well-known expansions of the logarithm and the exponential
of a power series. We show that it is advantageous to the Panjer recursion
advocated in the original CreditRisk
document, in that it is numerically stable. The crucial stability arguments are explained in detail. Furthermore, the
computational complexity of the resulting algorithm is stated.
We introduce a new Monte Carlo method for constructing the exercise
boundary of an American option in a generalized Black-Scholes framework.
Based on a known exercise boundary, it is shown how to price and hedge the
American option by Monte Carlo simulation of suitable probabilistic represen-
tations in connection with the respective parabolic boundary value problem.
The methods presented are supported by numerical simulation experiments.
The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check.
With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn
can be used to characterize the phenomenon of noise-induced resonance.
Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristic developed for the reduced model can thus be applied to the original model.
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check. With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance. Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristic developed for the reduced model can thus be applied to the original model.
This paper is concerned with the study of insurance related derivatives on financial markets that are based on non-tradable underlyings, but are correlated with tradable assets. We calculate exponential utility-based indifference prices, and corresponding derivative hedges. We use the fact that they can be represented in terms of solutions of forward-backward stochastic differential equations (FBSDE) with quadratic growth generators. We derive the Markov property of such FBSDE and generalize results on the differentiability relative to the initial value of their forward components. In this case the optimal hedge can be represented by the price gradient multiplied with the correlation coefficient. This way we obtain a generalization of the classical ‘delta hedge’ in complete markets.