156 research outputs found
Some remarks on first passage of Levy processes, the American put and pasting principles
The purpose of this article is to provide, with the help of a fluctuation
identity, a generic link between a number of known identities for the first
passage time and overshoot above/below a fixed level of a Levy process and the
solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and
Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript
(1999), SIAM J. Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished
manuscript (2000)], Avram, Chan and Usabel [Stochastic Process. Appl. 100
(2002) 75-107], Mordecki [Finance Stoch. 6 (2002) 473-493], Asmussen, Avram and
Pistorius [Stochastic Process. Appl. 109 (2004) 79-111] and Chesney and
Jeanblanc [Appl. Math. Fin. 11 (2004) 207-225] to the American perpetual put
optimal stopping problem. Furthermore, we make folklore precise and give
necessary and sufficient conditions for smooth pasting to occur in the
considered problem.Comment: Published at http://dx.doi.org/10.1214/105051605000000377 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
On a Fluctuation Identity for Random Walks and Lévy Processes
In this paper, some identities in laws involving ladder processes for random walks and Lévy processes are extended and unified. 2000 Mathematics Subject Classification 60G50, 60G51 (primary), 60G17 (secondary
Boundary-crossing identities for diffusions having the time-inversion property
We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family
Average trajectory of returning walks
We compute the average shape of trajectories of some one--dimensional
stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between
two successive returns to a reference value, finding that it obeys a scaling
form. For uncorrelated random walks the average shape is semicircular,
independently from the single increments distribution, as long as it is
symmetric. Such universality extends to biased random walks and Levy flights,
with the exception of a particular class of biased Levy flights. Adding a
linear damping term destroys scaling and leads asymptotically to flat
excursions. The introduction of short and long ranged noise correlations
induces non trivial asymmetric shapes, which are studied numerically.Comment: 16 pages, 16 figures; accepted for publication in Phys. Rev.
Cr cluster characterization in Cu-Cr-Zr alloy after ECAP processing and aging using SANS and HAADF-STEM
International audienceThe precipitation of nano-sized Cr clusters was investigated in a commercial Cu-1Cr-0.1Zr (wt.%) alloy processed by Equal-Channel Angular Pressing (ECAP) and subsequent aging at 550 °C for 4 hours using small angle neutron scattering (SANS) measurements and high-angle annular dark-field-scanning transmission electron microscopy (HAADF-STEM). The size and volume fraction of nano-sized Cr clusters were estimated using both techniques. These parameters assessed from SANS (d~3.2 nm, Fv~1.1 %) agreed reasonably with those from HAADF-STEM (d ~2.5 nm, Fv~2.3%). Besides nano-sized Cr clusters, HAADF-STEM technique evidenced the presence of rare cuboid and spheroid sub-micronic Cr particles about 380-620 nm mean size. Both techniques did not evidence the presence of intermetallic CuxZry phases within the aging conditions
Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift
We obtain exact asymptotic results for the disorder averaged persistence of a
Brownian particle moving in a biased Sinai landscape. We employ a new method
that maps the problem of computing the persistence to the problem of finding
the energy spectrum of a single particle quantum Hamiltonian, which can be
subsequently found. Our method allows us analytical access to arbitrary values
of the drift (bias), thus going beyond the previous methods which provide
results only in the limit of vanishing drift. We show that on varying the
drift, the persistence displays a variety of rich asymptotic behaviors
including, in particular, interesting qualitative changes at some special
values of the drift.Comment: 17 pages, two eps figures (included
Cost-effectiveness of twice-weekly versus once-weekly sessions of cognitive-behavioural therapy and interpersonal psychotherapy for depression at 12 months after start of treatment : randomised controlled trial
BACKGROUND: Cost-effective treatments are needed to reduce the burden of depression. One way to improve the cost-effectiveness of psychotherapy might be to increase session frequency, but keep the total number of sessions constant. AIM: To evaluate the cost-effectiveness of twice-weekly compared with once-weekly psychotherapy sessions after 12 months, from a societal perspective. METHOD: An economic evaluation was conducted alongside a randomised controlled trial comparing twice-weekly versus once-weekly sessions of psychotherapy (cognitive-behavioural therapy or interpersonal psychotherapy) for depression. Missing data were handled by multiple imputation. Statistical uncertainty was estimated with bootstrapping and presented with cost-effectiveness acceptability curves. RESULTS: Differences between the two groups in depressive symptoms, physical and social functioning, and quality-adjusted life-years (QALY) at 12-month follow-up were small and not statistically significant. Total societal costs in the twice-weekly session group were higher, albeit not statistically significantly so, than in the once-weekly session group (mean difference €2065, 95% CI -686 to 5146). The probability that twice-weekly sessions are cost-effective compared with once-weekly sessions was 0.40 at a ceiling ratio of €1000 per point improvement in Beck Depression Inventory-II score, 0.32 at a ceiling ratio of €50 000 per QALY gained, 0.23 at a ceiling ratio of €1000 per point improvement in physical functioning score and 0.62 at a ceiling ratio of €1000 per point improvement in social functioning score. CONCLUSIONS: Based on the current results, twice-weekly sessions of psychotherapy for depression are not cost-effective over the long term compared with once-weekly sessions
Adipocyte ATP-binding cassette G1 promotes triglyceride storage, fat mass growth, and human obesity
The role of ATP-binding Cassette G1 (ABCG1) transporter in human pathophysiology is still largely unknown. Indeed, beyond its role in mediating free cholesterol efflux to HDL, ABCG1 transporter equally promotes lipid accumulation in a triglyceride (TG)-rich environment through regulation of the bioavailability of Lipoprotein Lipase (LPL).As both ABCG1 and LPL are expressed in adipose tissue, we hypothesize that ABCG1 is implicated in adipocyte TG storage and could be then a major actor in adipose tissue fat accumulation.Silencing of Abcg1 expression by RNAi in 3T3-L1 preadipocytes compromised LPL-dependent TG accumulation during initial phase of differentiation. Generation of stable Abcg1 Knockdown 3T3-L1 adipocytes revealed that Abcg1 deficiency reduces TG storage and diminishes lipid droplet size through inhibition of Pparγ expression. Strikingly, local inhibition of adipocyte Abcg1 in adipose tissue from mice fed a high fat diet led to a rapid decrease of adiposity and weight gain. Analysis of two frequent ABCG1 SNPs (rs1893590 (A/C) and rs1378577 (T/G)) in morbidly obese individuals indicated that elevated ABCG1 expression in adipose tissue was associated with an increased PPARγ expression and adiposity concomitant to an increased fat mass and BMI (haplotype AT>GC). The critical role of ABCG1 regarding obesity was further confirmed in independent populations of severe obese and diabetic obese individuals.For the first time, this study identifies a major role of adipocyte ABCG1 in adiposity and fat mass growth and suggests that adipose ABCG1 might represent a potential therapeutic target in obesity
Optimal Stopping in Levy Models, for Non-Monotone Discontinuous Payoffs
We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an
embedded option to exit
American Step-Up and Step-Down Default Swaps under Levy Models
This paper studies the valuation of a class of default swaps with the
embedded option to switch to a different premium and notional principal anytime
prior to a credit event. These are early exercisable contracts that give the
protection buyer or seller the right to step-up, step-down, or cancel the swap
position. The pricing problem is formulated under a structural credit risk
model based on Levy processes. This leads to the analytic and numerical studies
of several optimal stopping problems subject to early termination due to
default. In a general spectrally negative Levy model, we rigorously derive the
optimal exercise strategy. This allows for instant computation of the credit
spread under various specifications. Numerical examples are provided to examine
the impacts of default risk and contractual features on the credit spread and
exercise strategy.Comment: 35 pages, 5 figure
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