General smile asymptotics with bounded maturity

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [Math. Finance 19 (2009), 1-12]. We present applications to popular models, including Carr-Wu finite moment logstable model, Merton's jump diffusion model and Heston's model.Comment: 35 pages, 2 figures. To appear on SIAM Journal on Financial Mathematic

Inner-Eye: Appearance-based Detection of Computer Scams

As more and more inexperienced users gain Internet access, fraudsters are attempting to take advantage of them in new ways. Instead of sophisticated exploitation techniques, simple confidence tricks can be used to create malware that is both very effective and likely to evade detection by traditional security software. Heuristics that detect complex malicious behavior are powerless against some common frauds. This work explores the use of imaging and text-matching techniques to detect typical computer scams such as pharmacy and rogue antivirus frauds. The Inner-Eye system implements the chosen approach in a scalable and efficient manner through the use of virtualization

Evolution of the Wasserstein distance between the marginals of two Markov processes

International audienceIn this paper, we are interested in the time derivative of the Wasserstein distance between the marginals of two Markov processes. As recalled in the introduction, the Kantorovich duality leads to a natural candidate for this derivative. Up to the sign, it is the sum of the integrals with respect to each of the two marginals of the corresponding generator applied to the corresponding Kantorovich potential. For pure jump processes with bounded intensity of jumps, we prove that the evolution of the Wasserstein distance is actually given by this candidate. In dimension one, we show that this remains true for Piecewise Deterministic Markov Processes

Sampling of probability measures in the convex order by Wasserstein projection

International audienceMotivated by the approximation of Martingale Optimal Transport problems, westudy sampling methods preserving the convex order for two probability measures$\mu$ and $\nu$ on $\mathbb{R}^d$, with $\nu$ dominating $\mu$. When$(X_i)_{1\le i\le I}$ (resp. $(Y_j)_{1\le j\le J}$) are i.i.d. according $\mu$(resp. $\nu$), the empirical measures $\mu_I$ and $\nu_J$ are not in the convexorder. We investigate modifications of $\mu_I$ (resp. $\nu_J$) smaller than$\nu_J$ (resp. greater than $\mu_I$) in the convex order and weakly convergingto $\mu$ (resp. $\nu$) as $I,J\to\infty$. In dimension 1, according to Kertzand R\"osler (1992), the set of probability measures with a finite first ordermoment is a lattice for the increasing and the decreasing convex orders. Fromthis result, we can define $\mu\vee\nu$ (resp. $\mu\wedge\nu$) that is greaterthan $\mu$ (resp. smaller than $\nu$) in the convex order. We give efficientalgorithms permitting to compute $\mu\vee\nu$ and $\mu\wedge\nu$ when $\mu$ and$\nu$ are convex combinations of Dirac masses. In general dimension, when $\mu$and $\nu$ have finite moments of order $\rho\ge 1$, we define the projection$\mu\curlywedge_\rho \nu$ (resp. $\mu\curlyvee_\rho\nu$) of $\mu$ (resp. $\nu$)on the set of probability measures dominated by $\nu$ (resp. larger than $\mu$)in the convex order for the Wasserstein distance with index $\rho$. When$\rho=2$, $\mu_I\curlywedge_2 \nu_J$ can be computed efficiently by solving aquadratic optimization problem with linear constraints. It turns out that, indimension 1, the projections do not depend on $\rho$ and their quantilefunctions are explicit, which leads to efficient algorithms for convexcombinations of Dirac masses. Last, we illustrate by numerical experiments theresulting sampling methods that preserve the convex order and their applicationto approximate Martingale Optimal Transport problems

Sampling of one-dimensional probability measures in the convex order and computation of robust option price bounds

This paper is an updated version of a part of the paper https://hal.archives-ouvertes.fr/hal-01589581 (or https://arxiv.org/pdf/1709.05287.pdf )International audienceFor µ and ν two probability measures on the real line such that µ is smaller than ν in the convex order, this property is in general not preserved at the level of the empirical measures µI = 1 I I i=1 δX i and νJ = 1 J J j=1 δY j , where (Xi) 1≤i≤I (resp. (Yj) 1≤j≤J) are independent and identically distributed according to µ (resp. ν). We investigate modifications of µI (resp. νJ) smaller than νJ (resp. greater than µI) in the convex order and weakly converging to µ (resp. ν) as I, J → ∞. According to Kertz and Rösler (1992), the set of probability measures on the real line with a finite first order moment is a complete lattice for the increasing and the decreasing convex orders. For µ and ν in this set, this enables us to define a probability measure µ ∨ ν (resp. µ ∧ ν) greater than µ (resp. smaller than ν) in the convex order. We give efficient algorithms permitting to compute µ ∨ ν and µ ∧ ν (and therefore µI ∨ νJ and µI ∧ νJ) when µ and ν have finite supports. Last, we illustrate by numerical experiments the resulting sampling methods that preserve the convex order and their application to approximate martingale optimal transport problems and in particular to calculate robust option price bounds

What the App is That? Deception and Countermeasures in the Android User Interface

Abstract—Mobile applications are part of the everyday lives of billions of people, who often trust them with sensitive information. These users identify the currently focused app solely by its visual appearance, since the GUIs of the most popular mobile OSes do not show any trusted indication of the app origin. In this paper, we analyze in detail the many ways in which Android users can be confused into misidentifying an app, thus, for instance, being deceived into giving sensitive information to a malicious app. Our analysis of the Android platformAPIs, assisted by an automated state-exploration tool, led us to identify and categorize a variety of attack vectors (some previously known, others novel, such as a non-escapable fullscreen overlay) that allow a malicious app to surreptitiously replace or mimic the GUI of other apps and mount phishing and click-jacking attacks. Limitations in the system GUI make these attacks significantly harder to notice than on a desktop machine, leaving users completely defenseless against them. To mitigate GUI attacks, we have developed a two-layer defense. To detect malicious apps at the market level, we developed a tool that uses static analysis to identify code that could launch GUI confusion attacks. We show how this tool detects apps that might launch GUI attacks, such as ransomware programs. Since these attacks are meant to confuse humans, we have also designed and implemented an on-device defense that addresses the underlying issue of the lack of a security indicator in the Android GUI. We add such an indicator to the system navigation bar; this indicator securely informs users about the origin of the app with which they are interacting (e.g., the PayPal app is backed by “PayPal, Inc.”). We demonstrate the effectiveness of our attacks and the proposed on-device defense with a user study involving 308 human subjects, whose ability to detect the attacks increased significantly when using a system equipped with our defense. I