929 research outputs found
Regularization independent of the noise level: an analysis of quasi-optimality
The quasi-optimality criterion chooses the regularization parameter in
inverse problems without taking into account the noise level. This rule works
remarkably well in practice, although Bakushinskii has shown that there are
always counterexamples with very poor performance. We propose an average case
analysis of quasi-optimality for spectral cut-off estimators and we prove that
the quasi-optimality criterion determines estimators which are rate-optimal
{\em on average}. Its practical performance is illustrated with a calibration
problem from mathematical finance.Comment: 18 pages, 3 figure
Functional and Banach Space Stochastic Calculi: Path-Dependent Kolmogorov Equations Associated with the Frame of a Brownian Motion
First, we revisit basic theory of functional It\uf4/path-dependent calculus, using the formulation of calculus via regularization. Relations with the corresponding Banach space valued calculus are explored. The second part of the paper is devoted to the study of the Kolmogorov type equation associated with the so called window Brownian motion, called path-dependent heat equation, for which well-posedness at the level of strict solutions is established. Then, a notion of strong approximating solution, called strong-viscosity solution, is introduced which is supposed to be a substitution tool to the viscosity solution. For that kind of solution, we also prove existence and uniqueness
Impact of Investor's Varying Risk Aversion on the Dynamics of Asset Price Fluctuations
While the investors' responses to price changes and their price forecasts are
well accepted major factors contributing to large price fluctuations in
financial markets, our study shows that investors' heterogeneous and dynamic
risk aversion (DRA) preferences may play a more critical role in the dynamics
of asset price fluctuations. We propose and study a model of an artificial
stock market consisting of heterogeneous agents with DRA, and we find that DRA
is the main driving force for excess price fluctuations and the associated
volatility clustering. We employ a popular power utility function,
with agent specific and
time-dependent risk aversion index, , and we derive an approximate
formula for the demand function and aggregate price setting equation. The
dynamics of each agent's risk aversion index, (i=1,2,...,N), is
modeled by a bounded random walk with a constant variance . We show
numerically that our model reproduces most of the ``stylized'' facts observed
in the real data, suggesting that dynamic risk aversion is a key mechanism for
the emergence of these stylized facts.Comment: 17 pages, 7 figure
How Damage Diversification Can Reduce Systemic Risk
We consider the problem of risk diversification in complex networks. Nodes
represent e.g. financial actors, whereas weighted links represent e.g.
financial obligations (credits/debts). Each node has a risk to fail because of
losses resulting from defaulting neighbors, which may lead to large failure
cascades. Classical risk diversification strategies usually neglect network
effects and therefore suggest that risk can be reduced if possible losses
(i.e., exposures) are split among many neighbors (exposure diversification,
ED). But from a complex networks perspective diversification implies higher
connectivity of the system as a whole which can also lead to increasing failure
risk of a node. To cope with this, we propose a different strategy (damage
diversification, DD), i.e. the diversification of losses that are imposed on
neighboring nodes as opposed to losses incurred by the node itself. Here, we
quantify the potential of DD to reduce systemic risk in comparison to ED. For
this, we develop a branching process approximation that we generalize to
weighted networks with (almost) arbitrary degree and weight distributions. This
allows us to identify systemically relevant nodes in a network even if their
directed weights differ strongly. On the macro level, we provide an analytical
expression for the average cascade size, to quantify systemic risk.
Furthermore, on the meso level we calculate failure probabilities of nodes
conditional on their system relevance
Quality of Life and Personality Traits in Patients with Malignant Pleural Mesothelioma and Their First-Degree Caregivers.
Asbestos exposure causes significant pleural diseases, including malignant pleural mesothelioma (MPM). Taking into account the impact of MPM on emotional functioning and wellbeing, this study aimed to evaluate the quality of life and personality traits in patients with MPM and their first-degree caregivers through the World Health Organization Quality of Life–BREF (WHOQOL-BREF) and the Minnesota Multiphasic Personality Inventory-2 Restructured Form (MMPI-2-RF). The sample was composed of 27 MPM patients, 55 first-degree relatives enrolled in Casale Monferrato and Monfalcone (Italy), and 40 healthy controls (HC). Patients and relatives reported poorer physical health than the HC. Patients had a higher overall sense of physical debilitation and poorer health than relatives and the HC, more numerous complaints of memory problems and difficulties in concentrating, and a greater belief that goals cannot be reached or problems solved, while often claiming that they were more indecisive and inefficacious than the HC. First-degree relatives reported lower opinions of others, a greater belief that goals cannot be reached or problems solved, support for the notion that they are indecisive and inefficacious, and were more likely to suffer from fear that significantly inhibited normal activities than were HC. In multinomial regression analyses, partial models indicated that sex, physical comorbidities, and the True Response Inconsistency (TRIN-r), Malaise (MLS), and Behavior-Restricting Fears (BRF) dimensions of the MMPI-2-RF had significant effects on group differences. In conclusion, health care providers should assess the ongoing adjustment and emotional wellbeing of people with MPM and their relatives, and provide support to reduce emotional distress
Uncertainty in the Fluctuations of the Price of Stocks
We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as
an emerging market that has been affected by several political crises during
the recent years, and analyze the non-Gaussian probability density function
(PDF) of the log returns of the stocks' prices. We show that while the average
of the index did not fall very much over the time period of the study, its
day-to-day fluctuations strongly increased due to the crises. Using an approach
based on multiplicative processes with a detrending procedure, we study the
scale-dependence of the non-Gaussian PDFs, and show that the temporal
dependence of their tails indicates a gradual and systematic increase in the
probability of the appearance of large increments in the returns on approaching
distinct critical time scales over which the TEPIX has exhibited maximum
uncertainty.Comment: 5 pages, 5 figures. Accepted to appear in IJMP
Quantitative law describing market dynamics before and after interest-rate change
We study the behavior of U.S. markets both before and after U.S. Federal Open
Market Committee (FOMC) meetings, and show that the announcement of a U.S.
Federal Reserve rate change causes a financial shock, where the dynamics after
the announcement is described by an analogue of the Omori earthquake law. We
quantify the rate n(t) of aftershocks following an interest rate change at time
T, and find power-law decay which scales as n(t-T) (t-T)^-, with
positive. Surprisingly, we find that the same law describes the rate
n'(|t-T|) of "pre-shocks" before the interest rate change at time T. This is
the first study to quantitatively relate the size of the market response to the
news which caused the shock and to uncover the presence of quantifiable
preshocks. We demonstrate that the news associated with interest rate change is
responsible for causing both the anticipation before the announcement and the
surprise after the announcement. We estimate the magnitude of financial news
using the relative difference between the U. S. Treasury Bill and the Federal
Funds Effective rate. Our results are consistent with the "sign effect," in
which "bad news" has a larger impact than "good news." Furthermore, we observe
significant volatility aftershocks, confirming a "market underreaction" that
lasts at least 1 trading day.Comment: 16 pages (2-column), 9 Figures, 1 Table; Changes in final version
made in response to referee comment
Levy stable distributions via associated integral transform
We present a method of generation of exact and explicit forms of one-sided,
heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x <
\infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a
distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2,
3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta <
1, we obtain g_{\alpha \beta}(x). The method is based on the construction of
the integral operator, called Levy transform, which implements the above
operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this
manner many of the recently obtained exact results for g_{l/k}(x). This
approach can be also recast as an application of the Efros theorem for
generalized Laplace convolutions. It relies solely on efficient definite
integration.Comment: 12 pages, typos removed, references adde
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