1,721,009 research outputs found
Adaptive robust control with statistical learning
Full text linkIn stochastic control problems the agent chooses the optimal strategy to maximise or minimise the performance criterion. The performance criterion can be either the expectation of a reward function for the standard control problem or the non-linear expectation for the robust control problem. In parameterised stochastic control problems, the agent needs to know the value of the model parameters in the stochastic system to specify the optimal strategy correctly. However, it is hardly the case that the agent knows the values of the model parameters.
In this thesis, we aim to study a robust stochastic control problem where the agent does not know the values of the parameters of the underlying process. Therefore, we frame the stochastic control problem where we assume that the agent does not know the values of the model parameters. However, the agent uses the observable processes to estimate the values of the model parameters while simultaneously solving the stochastic control problem in a robust framework.
There are two key components in this new stochastic control problem. The first component is the parameter estimation part where the agent uses the realisation of the underlying process to estimate the unknown parameters in the stochastic system. We particularly focus on online parameter estimation. The online estimator is an important ingredient for our stochastic control problem because this type of estimator allows the agent to obtain the optimal strategy in feedback form. The second component is the stochastic control part which is the question of how to design a time-consistent stochastic control problem that allows the agent to also estimate the parameters and optimise her strategy simultaneously. In this thesis, we address each component of the problem above in the continuous-time setting and then the utility maximisation problem under this framework is studied carefully
Algorithmic collusion: theory & practice
Full text linkWe develop a framework to analyze the evolution of bounded memory strategies in a repeated game. In this framework, we introduce the algorithmic learning equations, a set of ordinary differential equations which characterizes the finite-time and asymptotic behavior of the stochastic interaction between learning algorithms that learn a bounded memory strategy in a repeated game. Our framework allows us to study repeated games under a variety of monitoring structures, including perfect, public, private, and any of the combinations. Using this framework, we use a dynamic generalization of smooth fictitious play with bounded m-memory strategies to model learning with bounded rationality that is consistent with learning by algorithms. With this learning model, we prove a Folk theorem when players with bounded rationality learn as they play a repeated potential game. In a repeated potential game with perfect monitoring, we use this learning model to show that for any feasible and individually rational payoff profile, if players have sufficient memory, are sufficiently patient, and best respond with sufficiently few mistakes, then the players have a non-zero probability of learning an m-memory strategy profile that achieves an average payoff close to the specified payoff profile for an appropriate continuation game. Moreover, the strategy profile learned is an m-memory ε-subgame perfect equilibrium of the repeated game. Finally, we examine a case study where high-frequency traders (HFTs) in the European ETF market break the pre-trade anonymity of limit orders by signaling their type in an otherwise anonymous market. We explain the behavior of HFTs with a model that considers competitive and collusive equilibria. The model shows that the behavior of the HFTs is consistent with that in a collusive equilibrium where HFTs signal themselves to avoid sniping each other's limit orders. Signaling enables the HFTs to share the benign flow from retail limit orders, and to share the additional benign flow from impatient investors who otherwise would have traded with a retail investor’s limit order
Uncertain execution in order-driven markets
Full text linkSo-called 'latency' refers to the various small but significant time delays that occur in the course of the communications between a trader and a market. Such delays happen between the time an exchange streams market data to a trader, the time at which the trader processes the information and decides to trade, and the time at which the exchange receives and processes the order from the trader. Latency is a challenge faced by all traders and is of great importance in modern financial markets. In the present work, we develop mathematical models to solve a variety of problems faced by liquidity takers regarding uncertainty in executions.
Firstly, we devise a model for computing the price that traders are willing to pay to reduce their latency. This latency-optimal strategy balances the tradeoff, over a period of time, between the costs of walking the limit order book and the percentage of orders filled. This work may lead to social benefits, since it offers a way to stop the arms race to being faster in the marketplace.
Secondly, we develop a latency-optimal trading strategy that improves the marksmanship of liquidity takers. We make use of the techniques of variational analysis to obtain the optimal price limit of each marketable limit order (MLO) that the trader sends. The price limit of each MLO is characterized as the solution to a new class of forward-backward stochastic differential equations (FBSDEs) driven by random measures. We prove the existence and uniqueness of the FBSDE solution and solve the FBSDE numerically to illustrate the performance of the strategies.
Finally, we show how traders can optimally liquidate a position over a trading window when there is latency in the marketplace. We frame our model as an impulse control problem with stochastic delay -- this work contributes to the stochastic control literature by allowing one to have random delays before the impulses take place. We show that impatient liquidity takers submit MLOs that may walk the book (capped by the limit price) to increase the probability of filling the trades. Patient traders who are fast do not use their speed to hit the quotes they observe, nor to finish the execution programme early: they use speed to complete the execution with as many speculative MLOs as possible. We use foreign exchange data to implement the random-latency-optimal strategy and to compare it with various benchmarks. We find that for patient traders, the random-latency optimal strategy outperforms the bechmarks that do not account for latency by a quantity that is greater than the transaction costs paid by liquidity takers. Around news announcements, the value of the outperformance significantly increases. The superiority of the latency-optimal strategies is due to both the speculative MLOs that are filled and the price protection of the MLOs
Incorporating sequential and geometric structure into deep neural networks
Full text linkModern deep learning models have achieved great success, but they struggle with structured inputs unless they ingest massive amounts of data, or are guided by inductive biases that reflect the data’s inherent sequential or geometric structure. This thesis focuses on improving model performance in settings like time series and graph-structured data, which are common in real-world domains such as finance or healthcare. In particular, it addresses key challenges in these domains, such as the presence of long-range dependencies, irregular sampling, over-smoothing, and over-squashing, aiming to design architectures that are both expressive, performant, and computationally efficient. We divide this work into two sections. The first section is concerned with learning from data with sequential structure, and tackles several well-known problems associated with using deep learning in this data modality. In the second section, we focus on geometric deep learning, where we build a bridge between the recurrent and graph deep learning worlds in §5, and also study an independent problem in the area of manifold learning. Firstly, in §3, we develop a deep survival analysis method for limit order books that leverages a convolutional-Transformer to generate latent representations and a monotonic neural network to abide by the constraints of the function being modelled. By integrating local convolutional filters with a self-attention mechanism and a right-censored log-likelihood loss, our approach effectively captures the complex temporal dynamics inherent in high-frequency financial data, yielding superior estimates of order fill probabilities compared to standard benchmarks. Next, in §4, we introduce Rough Transformers—a new architecture that integrates signature transforms into the Transformer model. By extracting both local and global signature features, the Rough Transformer efficiently models irregularly sampled time-series data while dramatically reducing computational cost. In the realm of graph neural networks, we revisit the over-smoothing and oversquashing phenomena by analyzing their connection with vanishing gradients in §5. We show that the contractive nature of normalized adjacency matrices leads to extreme gradient vanishing and representational collapse. By reinterpreting GNNs as state-space models, we introduce GNN-SSMs that provide explicit control over the layer-wise Jacobian spectrum. This state-space formulation mitigates over-smoothing and enhances long-range information propagation, effectively bridging ideas from recurrent and graph learning. Finally, in §6, we propose Neural Latent Geometry Search (NLGS), a framework for automatically identifying optimal latent space geometries. Modeling latent spaces as products of constant-curvature manifolds, we introduce a principled measure based on the Gromov–Hausdorff distance to compare candidate latent geometries. By constructing a geometry-informed graph search space and applying Bayesian optimization, our approach efficiently discovers the product manifold signature that best aligns with the underlying data structure, as demonstrated on tasks such as image reconstruction and latent graph inference. Collectively, these contributions seek to advance deep learning by integrating temporal and geometric inductive biases into network architectures, enhancing model expressiveness, scalability, and performance across diverse real-world applications
Statistical methods in financial market dynamics and portfolio strategies
Full text linkThis thesis uses statistical methods to explore topics in financial economics. In particular, we focus on topics related to financial market dynamics and portfolio strategies. This thesis makes four contributions to the literature.
First, we introduce a method to detect linear and nonlinear lead-lag relationships in stock returns that uses pairwise Lévy-area and cross-correlation to rank assets from leaders to followers. We construct portfolios by trading followers based on leaders’ prior returns, hedged with an SPY ETF. With data from 1963 to 2022 for over 500 stocks, our portfolios achieve annualized returns over 20% and Sharpe ratios over 2. The relationships we discover are only partially explained by traditional factors like size or sector. Our results support the slow information diffusion hypothesis as daily rebalanced portfolios outperform less frequently rebalanced ones.
Second, we study the effect of intraday volume shocks on stock returns during overnight and intraday periods. We discover a significant positive relationship between volume shocks and subsequent overnight returns, while no such effect exists during the next intra-day session. Well-known asset pricing risk factors and common explanations that associate abnormal trading volume with investor attention and cost of capital cannot account for the distinct intraday and overnight patterns we observe. We employ linear and machine learning models to forecast volume shocks and to construct portfolios that monetize the positive correlation between volume shocks and overnight stock returns. Our approach addresses the issue that volume shock is only known after the close auction; we show that this issue of non-tradability does not explain the observed relationship between volume shock and overnight stock returns.
Third, we propose a framework to construct statistical arbitrage portfolios with graph clustering algorithms. First, we use five clustering methods to partition the correlation matrix of market residual returns of stocks into clusters. Next, we construct and evaluate the performance of mean-reverting statistical arbitrage portfolios within each cluster. We show that our proposed framework generates profitable trading strategies with over 10% annualized returns and statistically significant Sharpe ratios above one. The performance of our statistical arbitrage portfolios is neutral to the market and cannot be fully explained by intra-industry mean-reversion effects.
In the last part, we examine the investment value in sell-side analyst price targets. We treat each analyst as a portfolio manager and use their price targets to construct 12-month implied return forecasts and self-financing long-short portfolios for each analyst. Our empirical analysis shows that while the average analyst does not generate statistically significant alpha relative to the returns of a long-only portfolio benchmark, a subset of analysts exhibits persistent alpha. Motivated by this heterogeneity, we introduce a “fund-of-analysts” framework that first predicts analyst performance and then dynamically allocates weights across analysts based on predicted analyst performances. Our results show that this meta-portfolio strategy can yield significant alpha over long-only benchmarks
Statistical learning of Hawkes models and market microstructure
Full text linkMultivariate Hawkes processes (MHP) are a fundamental class of point processes with self-excitation. When estimating parameters for these processes, a difficulty is that the two main error functionals, the log-likelihood and the least squares error (LSE), as well as the evaluation of their gradients, have a quadratic complexity in the number of observed events. In practice, this prohibits the use of exact gradient-based algorithms for parameter estimation in many settings. Furthermore, MHP models are not designed for non-stationary training data, and they cannot incorporate event information besides their timestamps: we introduce the marked time-dependent linear Hawkes (MTLH) model to overcome these limitations. We construct an adaptive stratified sampling estimator of the gradient of the LSE of Hawkes models. This results in the ASLSD algorithm, a fast parametric estimation method for MHP and MTLH with general kernels, applicable to large datasets, which compares favourably with existing methods. We evaluate our algorithm on synthetic and real-world data.
We use the ASLSD algorithm to model high-frequency mid-price movements in the Nasdaq equities market using Hawkes models with multi-modal kernels, time varying baselines and multidimensional continuous marks. This approach allows us to capture the different frequencies of excitation of price movements, and the non-Markovian, non-stationary nature of price changes, while getting a better fit to market data. We leverage the branching representation of fitted models to build a counterfactual price impact model, and to understand exogenous price movements
Analysis of online learning algorithms in machine learning
Full text linkIn this thesis, we consider the problem that optimizes the parameter in the stationary distribution of markov decision process, stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs). First, we study the online Actor-critic algorithms in Reinforcement Learning with tabular parametrization and prove that, under a time rescaling, the algorithm converges to ordinary differential equations (ODEs) as the number of updates becomes large. The convergence and convergence rate to the optimal strategies are given by using a two time-scale analysis which asymptotically decouples the critic ODE from the actor ODE. Next, under the same framework, we show that when both the actor and critic are parameterized by single-layer neural networks, the Actor-critic algorithm will converge in distribution to a system of ODEs with random initial conditions as the number of hidden units and the number of training steps goes to infinity. The convergence to a stationary point of the limit actor network is also established. Further, we develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of SDE models. The novel idea of our algorithm is that the gradient estimate is simultaneously updated using forward propagation of the SDE state derivatives, which asymptotically converges to the direction of steepest descent. We rigorously prove convergence of the online forward propagation algorithm for linear SDE models and present its numerical results to a range of mathematical finance applications. Finally, we establish the convergence of our algorithm for a class of nonlinear dissipative SDEs whose drift and volatility functions both depend upon the parameters which are being optimized. We also show the application of our algorithm in Neural SPDEs
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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