We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. This resilience is modeled through a potentially arbitrary limit-order book shape. T
Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for “calibration-on-the-fly”, typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this limit is a well-known problem in the field; the general case is
The prediction of foreign exchange rates, such as the US Dollar (USD) to Bangladeshi Taka (BDT), plays a pivotal role in global financial markets, influencing trade, investments, and economic stability. This study leverages historical USD/BDT exchange rate data from 2018 to 2023, sourced from Yahoo
We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determin
In April 2020, the Chicago Mercantile Exchange temporarily switched the pricing formula for West Texas Intermediate oil market options from the Black model to the Bachelier model. In this context, we introduce an additive Bachelier model that provides a simple closed-form solution and a good descrip
In cryptocurrency markets, a key challenge for perpetual future issuers is maintaining alignment between the perpetual future price and target value. This study addresses this challenge by exploring the relationship between funding rates and perpetual future prices. Our results demonstrate that by a
Financial analysis presents complex challenges that could leverage large language model (LLM) capabilities. However, the scarcity of challenging financial datasets, particularly for Japanese financial data, impedes academic innovation in financial analytics. As LLMs advance, this lack of accessible
Financial decision-making presents unique challenges for language models, demanding temporal reasoning, adaptive risk assessment, and responsiveness to dynamic events. While large language models (LLMs) show strong general reasoning capabilities, they often fail to capture behavioral patterns centra
This paper investigates the optimal hedging strategies of an informed broker interacting with multiple traders in a financial market. We develop a theoretical framework in which the broker, possessing exclusive information about the drift of the asset’s price, engages with traders whose trading acti
This document analyzes price discovery in cryptocurrency markets by comparing centralized and decentralized exchanges, as well as spot and futures markets. The study focuses first on Ethereum (ETH) and then applies a similar approach to Bitcoin (BTC). Chapter 1 outlines the theoretical framework, em
Accurate electricity price forecasting (EPF) is crucial for effective decision-making in power trading on the spot market. While recent advances in generative artificial intelligence (GenAI) and pre-trained large language models (LLMs) have inspired the development of numerous time series foundation
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing concepts of comonotonicity and single-point concentration.
The discrepancy between realized volatility and the market’s view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast’s ability to predict firm-level volatility. We consider this phenomenon at the dai
We investigate the asymptotic behaviour of the implied volatility in the Bachelier setting, extending the large-strike results established for the Black-Scholes framework. Exploiting the theory of regular variation, we derive explicit expressions for the Bachelier implied volatility in the wings of
We develop a framework for stochastic portfolio theory (SPT), which incorporates modern nonlinear price impact and impact decay models. Our main result is the derivation of the celebrated master formula for additive functional generation of trading strategies in a general high-dimensional market mod
We introduce a novel proxy for firm linkages, Characteristic Vector Linkages (CVLs). We use this concept to estimate firm linkages, first through Euclidean similarity, and then by applying Quantum Cognition Machine Learning (QCML) to similarity learning. We demonstrate that both methods can be used
In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous “square-root law” of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the linear impact of order imbalances? Can one entirely explain
This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity, continuity, and independence-enabling machine-verified proofs of bo
We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences r
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on