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Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process.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&gt;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

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