Scaling limit of a limit order book model via the regenerative characterization of L\'evy trees

We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a new atom is added at a random distance from the rightmost atom. Interpreting atoms as limit buy orders, this process was introduced by Lakner et al. to model a one-sided limit order book. We consider this model in the regime where the total number of orders converges to a reflected Brownian motion, and complement the results of Lakner et al. by showing that, in the case where the mean displacement at which a new order is added is positive, the measure-valued process describing the whole limit order book converges to a simple functional of this reflected Brownian motion. Our results make it possible to derive useful and explicit approximations on various quantities of interest such as the depth or the total value of the book. Our approach leverages an unexpected connection with L\'evy trees. More precisely, the cornerstone of our approach is the regenerative characterization of L\'evy trees due to Weill, which provides an elegant proof strategy which we unfold.Comment: Accepted for publication in stochastic system

Optimal trading strategy for an investor: the case of partial information

AbstractWe shall address here the optimization problem of an investor who wants to maximize the expected utility from terminal wealth. The novelty of this paper is that the drift process and the driving Brownian motion appearing in the stochastic differential equation for the security prices are not assumed to be observable for investors in the market. Investors observe security prices and interest rates only. The drift process will be modelled by a Gaussian process, which in a special case becomes a multi-dimensional mean-reverting Ornstein–Uhlenbeck process. The main result of the paper is an explicit representation for the optimal trading strategy for a wide range of utility functions

Utility maximization with partial information

AbstractIn the present paper we address two maximization problems: the maximization of expected total utility from consumption and the maximization of expected utility from terminal wealth. The price process of the available financial assets is assumed to satisfy a system of functional stochastic differential equations. The difference between this paper and the existing papers on the same subject is that here we require the consumption and investment processes to be adapted to the natural filtration of the price processes. This requirement means that the only available information for agents in this economy at a certain time are the prices of the financial assets up to that time. The underlying Brownian motion and the drift process in the system of equations for the asset prices are not directly observable. Particular details will be worked out for the “Bayesian” example, when the dispersion coefficient is a fixed invertible matrix and the drift vector is an Fo-measurable, unobserved random variable with known distribution

On the roughness of the paths of RBM in a wedge

Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in ℝ2 is given in polar coordinates by S = {(r, θ) : r ≥ 0, 0 ≤ θ ≤ ξ } for some 0 α, the strong p-variation of the sample paths of Y is finite on compact intervals, and, for 0 < p ≤ α, the strong p-variation of Y is infinite on [0,T ] whenever Z has been started from the origin. We also show that on excursion intervals of Z away from the origin, (Z,Y ) satisfies the standard Skorokhod problem for X. However, on the entire time horizon (Z,Y ) does not satisfy the standard Skorokhod problem for X, but nevertheless we show that it satisfies the extended Skorkohod problem

Action needed for the EU Common Agricultural Policy to address sustainability challenges

Abstract Making agriculture sustainable is a global challenge. In the European Union (EU), the Common Agricultural Policy (CAP) is failing with respect to biodiversity, climate, soil, land degradation as well as socio-economic challenges. The European Commission's proposal for a CAP post-2020 provides a scope for enhanced sustainability. However, it also allows Member States to choose low-ambition implementation pathways. It therefore remains essential to address citizens' demands for sustainable agriculture and rectify systemic weaknesses in the CAP, using the full breadth of available scientific evidence and knowledge. Concerned about current attempts to dilute the environmental ambition of the future CAP, and the lack of concrete proposals for improving the CAP in the draft of the European Green Deal, we call on the European Parliament, Council and Commission to adopt 10 urgent action points for delivering sustainable food production, biodiversity conservation and climate mitigation. Knowledge is available to help moving towards evidence-based, sustainable European agriculture that can benefit people, nature and their joint futures. The statements made in this article have the broad support of the scientific community, as expressed by above 3,600 signatories to the preprint version of this manuscript. The list can be found here (https://doi.org/10.5281/zenodo.3685632). A free Plain Language Summary can be found within the Supporting Information of this article.Peer reviewe

Impact of safety-related dose reductions or discontinuations on sustained virologic response in HCV-infected patients: Results from the GUARD-C Cohort

BACKGROUND: Despite the introduction of direct-acting antiviral agents for chronic hepatitis C virus (HCV) infection, peginterferon alfa/ribavirin remains relevant in many resource-constrained settings. The non-randomized GUARD-C cohort investigated baseline predictors of safety-related dose reductions or discontinuations (sr-RD) and their impact on sustained virologic response (SVR) in patients receiving peginterferon alfa/ribavirin in routine practice. METHODS: A total of 3181 HCV-mono-infected treatment-naive patients were assigned to 24 or 48 weeks of peginterferon alfa/ribavirin by their physician. Patients were categorized by time-to-first sr-RD (Week 4/12). Detailed analyses of the impact of sr-RD on SVR24 (HCV RNA <50 IU/mL) were conducted in 951 Caucasian, noncirrhotic genotype (G)1 patients assigned to peginterferon alfa-2a/ribavirin for 48 weeks. The probability of SVR24 was identified by a baseline scoring system (range: 0-9 points) on which scores of 5 to 9 and <5 represent high and low probability of SVR24, respectively. RESULTS: SVR24 rates were 46.1% (754/1634), 77.1% (279/362), 68.0% (514/756), and 51.3% (203/396), respectively, in G1, 2, 3, and 4 patients. Overall, 16.9% and 21.8% patients experienced 651 sr-RD for peginterferon alfa and ribavirin, respectively. Among Caucasian noncirrhotic G1 patients: female sex, lower body mass index, pre-existing cardiovascular/pulmonary disease, and low hematological indices were prognostic factors of sr-RD; SVR24 was lower in patients with 651 vs. no sr-RD by Week 4 (37.9% vs. 54.4%; P = 0.0046) and Week 12 (41.7% vs. 55.3%; P = 0.0016); sr-RD by Week 4/12 significantly reduced SVR24 in patients with scores <5 but not 655. CONCLUSIONS: In conclusion, sr-RD to peginterferon alfa-2a/ribavirin significantly impacts on SVR24 rates in treatment-naive G1 noncirrhotic Caucasian patients. Baseline characteristics can help select patients with a high probability of SVR24 and a low probability of sr-RD with peginterferon alfa-2a/ribavirin