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This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for…

In this paper we explore the usage of deep reinforcement learning algorithms to automatically generate consistently profitable, robust, uncorrelated trading signals in any general financial market. In order to do this, we present a novel…

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive Control (MPC) scheme, recently introduced in [2], when restricted to the class of…

In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…

Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture.…

Conformal prediction offers finite-sample coverage guarantees under minimal assumptions. However, existing methods treat the entire modeling process as a black box, overlooking opportunities to exploit and understand modular structure. We…

We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in…

Predictive process monitoring focuses on forecasting future states of ongoing process executions, such as predicting the outcome of a particular case. In recent years, the application of machine learning models in this domain has garnered…

In this work, we study some novel applications of conformal inference techniques to the problem of providing machine learning procedures with more transparent, accurate, and practical performance guarantees. We provide a natural extension…

This paper introduces the factorial marked temporal point process model and presents efficient learning methods. In conventional (multi-dimensional) marked temporal point process models, event is often encoded by a single discrete variable…

Market equilibria of matching markets offer an intuitive and fair solution for matching problems without money with agents who have preferences over the items. Such a matching market can be viewed as a variation of Fisher market, albeit…

Time-series forecasting is a critical challenge in various domains and has witnessed substantial progress in recent years. Many real-life scenarios, such as public health, economics, and social applications, involve feedback loops where…

Prediction markets show considerable promise for developing flexible mechanisms for machine learning. Here, machine learning markets for multivariate systems are defined, and a utility-based framework is established for their analysis. This…

Individuals are often influenced by the behavior of others, for instance because they wish to obtain the benefits of coordinated actions or infer otherwise inaccessible information. In such situations this social influence decreases the ex…

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…

We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and the corresponding market weights. These models substantially extend volatility…

This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only…

In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary…

Despite achieving promising fairness-error trade-offs, in-processing mitigation techniques for group fairness cannot be employed in numerous practical applications with limited computation resources or no access to the training pipeline of…