342 research outputs found
Utility maximization with random horizon: a BSDE approach
International audienceIn this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations
On arbitrages arising from honest times
In the context of a general continuous financial market model, we study
whether the additional information associated with an honest time gives rise to
arbitrage profits. By relying on the theory of progressive enlargement of
filtrations, we explicitly show that no kind of arbitrage profit can ever be
realised strictly before an honest time, while classical arbitrage
opportunities can be realised exactly at an honest time as well as after an
honest time. Moreover, stronger arbitrages of the first kind can only be
obtained by trading as soon as an honest time occurs. We carefully study the
behavior of local martingale deflators and consider no-arbitrage-type
conditions weaker than NFLVR.Comment: 25 pages, revised versio
Herding model and 1/f noise
We provide evidence that for some values of the parameters a simple agent
based model, describing herding behavior, yields signals with 1/f power
spectral density. We derive a non-linear stochastic differential equation for
the ratio of number of agents and show, that it has the form proposed earlier
for modeling of 1/f^beta noise with different exponents beta. The non-linear
terms in the transition probabilities, quantifying the herding behavior, are
crucial to the appearance of 1/f noise. Thus, the herding dynamics can be seen
as a microscopic explanation of the proposed non-linear stochastic differential
equations generating signals with 1/f^beta spectrum. We also consider the
possible feedback of macroscopic state on microscopic transition probabilities
strengthening the non-linearity of equations and providing more opportunities
in the modeling of processes exhibiting power-law statistics
Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
The Airy distribution function describes the probability distribution of the
area under a Brownian excursion over a unit interval. Surprisingly, this
function has appeared in a number of seemingly unrelated problems, mostly in
computer science and graph theory. In this paper, we show that this
distribution also appears in a rather well studied physical system, namely the
fluctuating interfaces. We present an exact solution for the distribution
P(h_m,L) of the maximal height h_m (measured with respect to the average
spatial height) in the steady state of a fluctuating interface in a one
dimensional system of size L with both periodic and free boundary conditions.
For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L
where the function f(x) is the Airy distribution function. This result is valid
for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the
free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}),
but the scaling function F(x) is different from that of the periodic case. We
compute this scaling function explicitly for the Edwards-Wilkinson interface
and call it the F-Airy distribution function. Numerical simulations are in
excellent agreement with our analytical results. Our results provide a rather
rare exactly solvable case for the distribution of extremum of a set of
strongly correlated random variables. Some of these results were announced in a
recent Letter [ S.N. Majumdar and A. Comtet, Phys. Rev. Lett., 92, 225501
(2004)].Comment: 27 pages, 10 .eps figures included. Two figures improved, new
discussion and references adde
Functionals of the Brownian motion, localization and metric graphs
We review several results related to the problem of a quantum particle in a
random environment.
In an introductory part, we recall how several functionals of the Brownian
motion arise in the study of electronic transport in weakly disordered metals
(weak localization).
Two aspects of the physics of the one-dimensional strong localization are
reviewed : some properties of the scattering by a random potential (time delay
distribution) and a study of the spectrum of a random potential on a bounded
domain (the extreme value statistics of the eigenvalues).
Then we mention several results concerning the diffusion on graphs, and more
generally the spectral properties of the Schr\"odinger operator on graphs. The
interest of spectral determinants as generating functions characterizing the
diffusion on graphs is illustrated.
Finally, we consider a two-dimensional model of a charged particle coupled to
the random magnetic field due to magnetic vortices. We recall the connection
between spectral properties of this model and winding functionals of the planar
Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and
conclusion added. Several references adde
Alternative approach to the optimality of the threshold strategy for spectrally negative Levy processes
Consider the optimal dividend problem for an insurance company whose
uncontrolled surplus precess evolves as a spectrally negative Levy process. We
assume that dividends are paid to the shareholders according to admissible
strategies whose dividend rate is bounded by a constant. The objective is to
find a dividend policy so as to maximize the expected discounted value of
dividends which are paid to the shareholders until the company is ruined.
Kyprianou, Loeffen and Perez [28] have shown that a refraction strategy (also
called threshold strategy) forms an optimal strategy under the condition that
the Levy measure has a completely monotone density. In this paper, we propose
an alternative approach to this optimal problem.Comment: 16 page
Affine term structure models : a time-changed approach with perfect fit to market curves
We address the so-called calibration problem which consists of fitting in a
tractable way a given model to a specified term structure like, e.g., yield or
default probability curves. Time-homogeneous jump-diffusions like Vasicek or
Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are
tractable processes but have limited flexibility; they fail to replicate actual
market curves. The deterministic shift extension of the latter (Hull-White or
JCIR++) is a simple but yet efficient solution that is widely used by both
academics and practitioners. However, the shift approach is often not
appropriate when positivity is required, which is a common constraint when
dealing with credit spreads or default intensities. In this paper, we tackle
this problem by adopting a time change approach. On the top of providing an
elegant solution to the calibration problem under positivity constraint, our
model features additional interesting properties in terms of implied
volatilities. It is compared to the shift extension on various credit risk
applications such as credit default swap, credit default swaption and credit
valuation adjustment under wrong-way risk. The time change approach is able to
generate much larger volatility and covariance effects under the positivity
constraint. Our model offers an appealing alternative to the shift in such
cases.Comment: 44 pages, figures and table
Gene expression profiling associated with the progression to poorly differentiated thyroid carcinomas
Poorly differentiated thyroid carcinomas (PDTC) represent a heterogeneous, aggressive entity, presenting features that suggest a progression from well-differentiated carcinomas. To elucidate the mechanisms underlying such progression and identify novel therapeutic targets, we assessed the genome-wide expression in normal and tumour thyroid tissues.info:eu-repo/semantics/publishe
5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote
Background: In the mouse zygote, DNA methylation patterns are heavily modified, and differ between the maternal and paternal pronucleus. Demethylation of the paternal genome has been described as an active and replication-independent process, although the mechanisms responsible for it remain elusive. Recently, 5-hydroxymethylcytosine has been suggested as an intermediate in this demethylation. Methodology/principal findings: In this study, we quantified DNA methylation and hydroxymethylation in both pronuclei of the mouse zygote during the replication period and we examined their patterns on the pericentric heterochromatin using 3D immuno-FISH. Our results demonstrate that 5-methylcytosine and 5-hydroxymethylcytosine localizations on the pericentric sequences are not complementary; indeed we observe no enrichment of either marks on some regions and an enrichment of both on others. In addition, we show that DNA demethylation continues during DNA replication, and is inhibited by aphidicolin. Finally, we observe notable differences in the kinetics of demethylation and hydroxymethylation; in particular, a peak of 5-hydroxymethylcytosine, unrelated to any change in 5-methylcytosine level, is observed after completion of replication. Conclusion/significance: Together our results support the already proposed hypothesis that 5-hydroxymethylcytosine is not a simple intermediate in an active demethylation process and could play a role of its own during early development
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