Related papers: Optimal Execution with Quadratic Variation Invento…
For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects,…
We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum…
Although behavioral economics has demonstrated that there are many situations where rational choice is a poor empirical model, it has so far failed to provide quantitative models of economic problems such as price formation. We make a step…
In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…
We study optimal trade execution strategies in financial markets with discrete order flow. The agent has a finite liquidation horizon and must minimize price impact given a random number of incoming trade counterparties. Assuming that the…
The motility of living things and synthetic self-propelled objects is often described using Active Brownian particles. To capture the interaction of these particles with their often complex environment, this model can be augmented with…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
We consider a ranking and selection (R&S) problem with the goal to select a system with the largest or smallest expected performance measure among a number of simulated systems with a pre-specified probability of correct selection. Fully…
To use control charts in practice, the in-control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured for example by the false alarm probability or the…
In this paper, we focus on multiple sampling problems for the estimation of the fractional Brownian motion when the maximum number of samples is limited, extending existing results in the literature in a non-Markovian framework. Two classes…
Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…
Time-varying volatility is an inherent feature of most economic time-series, which causes standard correlation estimators to be inconsistent. The quadrant correlation estimator is consistent but very inefficient. We propose a novel…
We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol…
We provide some theoretical extensions and a calibration protocol for our former dynamic optimal execution model. The Hawkes parameters and the propagator are estimated independently on financial data from stocks of the CAC40.…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…
We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also…
Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic…
The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated…
We make several improvements to the mean-variance framework for optimal pre-trade algorithmic execution, by working with volume measures and generic price dynamics. Volume measures are the continuum analogies for discrete volume profiles…