1,105 research outputs found
Asymptotic Conditional Distribution of Exceedance Counts: Fragility Index with Different Margins
Let be a random vector, whose components are not
necessarily independent nor are they required to have identical distribution
functions . Denote by the number of exceedances among
above a high threshold . The fragility index, defined by
if this limit exists, measures the
asymptotic stability of the stochastic system as the threshold
increases. The system is called stable if and fragile otherwise. In this
paper we show that the asymptotic conditional distribution of exceedance counts
(ACDEC) , , exists, if the
copula of is in the domain of attraction of a multivariate extreme
value distribution, and if
exists for
and some . This enables the computation of
the FI corresponding to and of the extended FI as well as of the
asymptotic distribution of the exceedance cluster length also in that case,
where the components of are not identically distributed
Theoretical Sensitivity Analysis for Quantitative Operational Risk Management
We study the asymptotic behavior of the difference between the values at risk
VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application
in sensitivity analysis of quantitative operational risk management within the
framework of the advanced measurement approach of Basel II (and III). Here L
describes the loss amount of the present risk profile and S describes the loss
amount caused by an additional loss factor. We obtain different types of
results according to the relative magnitudes of the thicknesses of the tails of
L and S. In particular, if the tail of S is sufficiently thinner than the tail
of L, then the difference between prior and posterior risk amounts VaR(L+S) -
VaR(L) is asymptotically equivalent to the expectation (expected loss) of S.Comment: 21 pages, 1 figure, 4 tables, forthcoming in International Journal of
Theoretical and Applied Finance (IJTAF
Risk margin for a non-life insurance run-off
For solvency purposes insurance companies need to calculate so-called best-estimate reserves for outstanding loss liability cash flows and a corresponding risk margin for non-hedgeable insurance-technical risks in these cash flows. In actuarial practice, the calculation of the risk margin is often not based on a sound model but various simplified methods are used. In the present paper we properly define these notions and we introduce insurance-technical probability distortions. We describe how the latter can be used to calculate a risk margin for non-life insurance run-off liabilities in a mathematically consistent way
How Heavy Are the Tails of a Stationary HARCH(k) Process? A Study of the Moments
How Heavy Are the Tails of a Stationary HARCH(k) Process? A Study of the Moment
On low-sampling-rate Kramers-Moyal coefficients
We analyze the impact of the sampling interval on the estimation of
Kramers-Moyal coefficients. We obtain the finite-time expressions of these
coefficients for several standard processes. We also analyze extreme situations
such as the independence and no-fluctuation limits that constitute useful
references. Our results aim at aiding the proper extraction of information in
data-driven analysis.Comment: 9 pages, 4 figure
Bridging the ARCH model for finance and nonextensive entropy
Engle's ARCH algorithm is a generator of stochastic time series for financial
returns (and similar quantities) characterized by a time-dependent variance. It
involves a memory parameter ( corresponds to {\it no memory}), and the
noise is currently chosen to be Gaussian. We assume here a generalized noise,
namely -Gaussian, characterized by an index
( recovers the Gaussian case, and corresponds to tailed
distributions). We then match the second and fourth momenta of the ARCH return
distribution with those associated with the -Gaussian distribution obtained
through optimization of the entropy S_{q}=\frac{% 1-\sum_{i} {p_i}^q}{q-1},
basis of nonextensive statistical mechanics. The outcome is an {\it analytic}
distribution for the returns, where an unique corresponds to each
pair ( if ). This distribution is compared with
numerical results and appears to be remarkably precise. This system constitutes
a simple, low-dimensional, dynamical mechanism which accommodates well within
the current nonextensive framework.Comment: 4 pages, 5 figures.Figure 4 fixe
Measuring degree-degree association in networks
The Pearson correlation coefficient is commonly used for quantifying the
global level of degree-degree association in complex networks. Here, we use a
probabilistic representation of the underlying network structure for assessing
the applicability of different association measures to heavy-tailed degree
distributions. Theoretical arguments together with our numerical study indicate
that Pearson's coefficient often depends on the size of networks with equal
association structure, impeding a systematic comparison of real-world networks.
In contrast, Kendall-Gibbons' is a considerably more robust measure
of the degree-degree association
Density of near-extreme events
We provide a quantitative analysis of the phenomenon of crowding of
near-extreme events by computing exactly the density of states (DOS) near the
maximum of a set of independent and identically distributed random variables.
We show that the mean DOS converges to three different limiting forms depending
on whether the tail of the distribution of the random variables decays slower
than, faster than, or as a pure exponential function. We argue that some of
these results would remain valid even for certain {\em correlated} cases and
verify it for power-law correlated stationary Gaussian sequences. Satisfactory
agreement is found between the near-maximum crowding in the summer temperature
reconstruction data of western Siberia and the theoretical prediction.Comment: 4 pages, 3 figures, revtex4. Minor corrections, references updated.
This is slightly extended version of the Published one (Phys. Rev. Lett.
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