Semimartingale
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Generalized Method of Integrated Moments for High-Frequency Data Open
We propose a semiparametric two-step inference procedure for a finite-dimensional parameter based on moment conditions constructed from high-frequency data. The population moment conditions take the form of temporally integrated functional…
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Non-homogeneous Random Walks: Lyapunov Function Methods for Near-Critical Stochastic Systems Open
A modern presentation of the 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks.
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Efficient estimation of integrated volatility functionals via multiscale jackknife Open
We propose semiparametrically efficient estimators for general integrated volatility functionals of multivariate semimartingale processes. A plug-in method that uses nonparametric estimates of spot volatilities is known to induce high-orde…
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Optimal investment with intermediate consumption under no unbounded profit with bounded risk Open
We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of th…
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Statistical estimation of the Oscillating Brownian Motion Open
We study the asymptotic behavior of estimators of a two-valued, discontinuous\ndiffusion coefficient in a Stochastic Differential Equation, called an\nOscillating Brownian Motion. Using the relation of the latter process with the\nSkew Bro…
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Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price Open
Pre-averaging is a popular strategy for mitigating microstructure in high frequency financial data. As the term suggests, transaction or quote data are averaged over short time periods ranging from 30 s to five min, and the resulting avera…
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A closed-form formula characterization of the Epps effect Open
In this study we provide an analytical characterization of the impact of zero returns on the popular realized covariance estimator of Barndorff-Nielsen and Shephard [Econometric analysis of realized covariation: High frequency based covari…
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Quadratic covariation estimation of an irregularly observed semimartingale with jumps and noise Open
This paper presents a central limit theorem for a pre-averaged version of the realized covariance estimator for the quadratic covariation of a discretely observed semimartingale with noise. The semimartingale possibly has jumps, while the …
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Markovian approximations of stochastic Volterra equations with the fractional kernel Open
We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is there…
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Continuous Time Analysis of Fleeting Discrete Price Moves Open
This article proposes a novel model of financial prices where (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tracta…
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Generalized density approach in progressive enlargement of filtrations Open
Motivated by credit risk modelling, we consider a type of default times whose probability law can have atoms, where standard intensity and density hypotheses in the enlargement of filtrations are not satisfied. We propose a generalized den…
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Stochastic integration with respect to cylindrical Lévy processes Open
A cylindrical Lévy process does not enjoy a cylindrical version of thesemimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral…
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KERNEL ESTIMATION OF SPOT VOLATILITY WITH MICROSTRUCTURE NOISE USING PRE-AVERAGING Open
We revisit the problem of estimating the spot volatility of an Itô semimartingale using a kernel estimator. A central limit theorem (CLT) with an optimal convergence rate is established for a general two-sided kernel. A new pre-averaging/k…
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A forward equation for barrier options under the Brunick & Shreve Markovian projection Open
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient de…
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On countably skewed Brownian motion with accumulation point Open
In this work we connect the theory of symmetric Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is perturbed by a series of constant multiples of local times at a s…
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Weak regularization by stochastic drift : Result and counter example Open
In this paper, we prove weak uniqueness of hypoelliptic stochastic\ndifferential equation with H{\\"o}lder drift, with H{\\"o}lder exponent strictly\ngreater than 1/3. We then extend to a weak framework the previous work [CdR12]\nwhere str…
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Nonparametric tests for detecting breaks in the jump behaviour of a time-continuous process Open
This paper is concerned with tests for changes in the jump behaviour of a time-continuous process. Based on results on weak convergence of a sequential empirical tail integral process, asymptotics of certain test statistics for breaks in t…
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Persistence and stability of the disease-free equilibrium in a stochastic epidemic model with imperfect vaccine Open
This paper concerns the dynamics of a stochastic SIVR epidemic model with imperfect vaccine where, differently from the epidemic model with perfect vaccine, the vaccinated is perturbed by the noise. This difference is the main difficulty t…
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Compactness criterion for semimartingale laws and semimartingale optimal transport Open
We provide a compactness criterion for the set of laws $ \\mathfrak{P}^{ac}_{sem}(\\Theta )$ on the Skorokhod space for which the canonical process $ X$ is a semimartingale having absolutely continuous characteristics with differential cha…
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Rough flows Open
We introduce in this work a concept of rough driver that somehow provides a rough path-like analogue of an enriched object associated with time-dependent vector fields. We use the machinery of approximate flows to build the integration the…
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Convex duality and Orlicz spaces in expected utility maximization Open
In this paper, we report further progress toward a complete theory of state‐independent expected utility maximization with semimartingale price processes for arbitrary utility function. Without any technical assumptions, we establish a sur…
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Optimal insider control and semimartingale decompositions under enlargement of filtration Open
We combine stochastic control methods, white noise analysis, and Hida–Malliavin calculus applied to the Donsker delta functional to obtain explicit representations of semimartingale decompositions under enlargement of filtrations. Some of …
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An Intuitive Introduction to Fractional and Rough Volatilities Open
Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm…
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Special weak Dirichlet processes and BSDEs driven by a random measure Open
This paper considers a forward BSDE driven by a random measure, when the\nunderlying forward process X is special semimartingale, or even more generally,\na special weak Dirichlet process. Given a solution (Y, Z, U), generally Y\nappears t…
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Unified signature cumulants and generalized Magnus expansions Open
The signature of a path can be described as its full non-commutative exponential. Following T. Lyons, we regard its expectation, the expected signature , as a path space analogue of the classical moment generating function. The logarithm t…
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The Euler Scheme for a Stochastic Differential Equation Driven by Pure Jump Semimartingales Open
In this paper we propose the asymptotic error distributions of the Euler scheme for a stochastic differential equation driven by Itô semimartingales. Jacod (2004) studied this problem for stochastic differential equations driven by pure ju…
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Estimating Jump Activity Using Multipower Variation Open
Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. This article shows how to build a simple and precise estimator of the jump activity index of a semimartinga…
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Local risk-minimization under restricted information on asset prices Open
In this paper we investigate the local risk-minimization approach for a semimartingale financial market where there are restrictions on the available information to agents who can observe at least the asset prices. We characterize the opti…
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Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework Open
We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective …
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ESTIMATING THE VOLATILITY OCCUPATION TIME VIA REGULARIZED LAPLACE INVERSION Open
We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled…