74 citations · 184 across the 30 of their papers we have counts for
44 papers
Universal portfolios in continuous time: an approach in pathwise Itô calculus
Xiyue Han, Alexander Schied
We provide a simple and straightforward approach to a continuous-time version of Cover's universal portfolio strategies within the model-free context of Föllmer's pathwise Itô calc…
On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models
Xiyue Han, Alexander Schied
In [Han \& Schied, 2023, \textit{arXiv 2307.02582}], an easily computable scale-invariant estimator was constructed to estimate the Hurst parameter of t…
Estimating the roughness exponent of stochastic volatility from discrete observations of the integrated variance
Xiyue Han, Alexander Schied
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion wit…
A criterion for absolute continuity relative to the law of fractional Brownian motion
Xiyue Han, Alexander Schied
Let be the sum of a fractional Brownian motion with Hurst parameter and an absolutely continuous and adapted drift process. We establish a simple criterion that guarantees…
Weierstrass Bridges
Alexander Schied, Zhenyuan Zhang
We introduce a new class of stochastic processes called fractional Wiener-Weierstrass bridges. They arise by applying the convolution from the construction of the classical, fracta…
Multiarmed Bandits Problem Under the Mean-Variance Setting
Hongda Hu, Arthur Charpentier, Mario Ghossoub +1
The classical multi-armed bandit (MAB) problem involves a learner and a collection of K independent arms, each with its own ex ante unknown independent reward distribution. At each…
Robust Faber--Schauder approximation based on discrete observations of an antiderivative
Xiyue Han, Alexander Schied
We study the problem of reconstructing the Faber--Schauder coefficients of a continuous function from discrete observations of its antiderivative . For instance, this questi…
The roughness exponent and its model-free estimation
Xiyue Han, Alexander Schied
Motivated by pathwise stochastic calculus, we say that a continuous real-valued function admits the roughness exponent if the variation of converges to…
A limit theorem for Bernoulli convolutions and the -variation of functions in the Takagi class
Xiyue Han, Alexander Schied, Zhenyuan Zhang
We consider a probabilistic approach to compute the Wiener--Young -variation of fractal functions in the Takagi class. Here, the -variation is understood as a generalization…
A probabilistic approach to the -variation of classical fractal functions with critical roughness
Xiyue Han, Alexander Schied, Zhenyuan Zhang
We consider Weierstraß and Takagi-van der Waerden functions with critical degree of roughness. In this case, the functions have vanishing variation for all bu…
A central bank strategy for defending a currency peg
Eyal Neuman, Alexander Schied, Chengguo Weng +1
We consider a central bank strategy for maintaining a two-sided currency target zone, in which an exchange rate of two currencies is forced to stay between two thresholds. To keep…
Step roots of Littlewood polynomials and the extrema of functions in the Takagi class
Xiyue Han, Alexander Schied
We give a new approach to characterizing and computing the set of global maximizers and minimizers of the functions in the Takagi class and, in particular, of the Takagi--Landsberg…
An FBSDE approach to market impact games with stochastic parameters
Samuel Drapeau, Peng Luo, Alexander Schied +1
We analyze a market impact game between risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market p…
On the variation of a class of fractal functions
Alexander Schied, Zhenyuan Zhang
The concept of the variation of a continuous function along a refining sequence of partitions is the key to a pathwise Itô integration theory with integrator $f…
Robustness in the Optimization of Risk Measures
Paul Embrechts, Alexander Schied, Ruodu Wang
We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement rel…
Nash equilibrium for risk-averse investors in a market impact game with transient price impact
Xiangge Luo, Alexander Schied
We consider a market impact game for risk-averse agents that are competing in a market model with linear transient price impact and additional transaction costs. For both finit…
On (signed) Takagi-Landsberg functions: variation, maximum, and modulus of continuity
Yuliya Mishura, Alexander Schied
We study a class of signed Takagi-Landsberg functions with Hurst parameter . We first show that the functions in admit a linear $p^{\text…
Protecting Pegged Currency Markets from Speculative Investors
Eyal Neuman, Alexander Schied
We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the…
On the minimizers of energy forms with completely monotone kernel
Alexander Schied, Elias Strehle
Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel…
Mild and viscosity solutions to semilinear parabolic path-dependent PDEs
Alexander Kalinin, Alexander Schied
We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appear…
Model-free portfolio theory and its functional master formula
Alexander Schied, Leo Speiser, Iryna Voloshchenko
We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework o…
The associativity rule in pathwise functional Itô calculus
Alexander Schied, Iryna Voloshchenko
In this paper we establish the associativity property of the pathwise Itô integral in a functional setting for continuous integrators. Here, associativity refers to the computation…
Domains of weak continuity of statistical functionals with a view toward robust statistics
Volker Krätschmer, Alexander Schied, Henryk Zähle
Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the cl…
Constructing functions with prescribed pathwise quadratic variation
Yuliya Mishura, Alexander Schied
We construct rich vector spaces of continuous functions with prescribed curved or linear pathwise quadratic variations. We also construct a class of functions whose quadratic varia…