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We review how to simulate continuous determinantal point processes (DPPs) and improve the current simulation algorithms in several important special cases as well as detail how certain types of conditional simulation can be carried out.…

We propose a novel method to improve estimation of asset returns for portfolio optimization. This approach first performs a monthly directional market forecast using an online decision tree. The decision tree is trained on a novel set of…

I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be…

Frontal photopolymerization (FPP) provides a versatile method for the rapid fabrication of solid polymer network materials by exposing photosensitive molecules to light. Dimensional control of structures created by this process is crucial…

Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…

The financial market trend forecasting method is emerging as a hot topic in financial markets today. Many challenges still currently remain, and various researches related thereto have been actively conducted. Especially, recent research of…

In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…

We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor…

Accurate forecasting in financial markets requires integrating diverse data sources, from historical prices to macroeconomic indicators and financial news. However, existing models often fail to align these modalities effectively, limiting…

An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…

While machine learning has witnessed significant advancements, the emphasis has largely been on data acquisition and model creation. However, achieving a comprehensive assessment of machine learning solutions in real-world settings…

We propose and study a planning problem we call Sequential Fault-Intolerant Process Planning (SFIPP). SFIPP captures a reward structure common in many sequential multi-stage decision problems where the planning is deemed successful only if…

I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…

Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of…

Modeling event sequences of multiple event types with marked temporal point processes (MTPPs) provides a principled way to uncover governing dynamical rules and predict future events. Current neural network approaches to MTPP inference rely…

In this article we derive partial differential equations (PDEs) for pricing interest rate derivatives under the generalized Forward Market Model (FMM) recently presented by A. Lyashenko and F. Mercurio in \cite{lyashenkoMercurio:Mar2019} to…

This paper analyses the forecasting performance of a new class of factor models with martingale difference errors (FMMDE) recently introduced by Lee and Shao (2018). The FMMDE makes it possible to retrieve a transformation of the original…

Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…