The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on $L^0$ is fixed to characterize the family of acceptable wealths that play the role of non negative financial
This article leverages deep reinforcement learning (DRL) to hedge American put options, utilizing the deep deterministic policy gradient (DDPG) method. The agents are first trained and tested with Geometric Brownian Motion (GBM) asset paths and demonstrate superior performance over traditional strat
This study explores the innovative use of Large Language Models (LLMs) as analytical tools for interpreting complex financial regulations. The primary objective is to design effective prompts that guide LLMs in distilling verbose and intricate regulatory texts, such as the Basel III capital requirem
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This generalizes previous results that used convexity, and also g
This study aims to analyze the impact of financial literacy, social capital and financial technology on financial inclusion. The research method used a quantitative research method, in which questionnaires were distributed to 100 active students in the economics faculty at 7 private colleges in Tang
This paper identifies the cryptocurrency market crashes and analyses its dynamics using the complex network. We identify three distinct crashes during 2017-20, and the analysis is carried out by dividing the time series into pre-crash, crash, and post-crash periods. Partial correlation based complex
Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the USA-China trade
One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based on Neural Networks to solve the Black-Scholes Equations. Real
In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) inf
We formulate a forward inflation index model with multi-factor volatility structure featuring a parametric form that allows calibration to correlations between indices of different tenors observed in the market. Assuming the nominal interest rate follows a single factor Gaussian short rate model, we
Investment portfolios, central to finance, balance potential returns and risks. This paper introduces a hybrid approach combining Markowitz’s portfolio theory with reinforcement learning, utilizing knowledge distillation for training agents. In particular, our proposed method, called KDD (Knowledge
This paper delves into financial markets that incorporate a novel form of heterogeneity among investors, specifically in terms of their beliefs regarding the reliability of signals in the business cycle economy model, which may be biased. Unlike most papers in this field, we not only analyze the equ
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a microsystem. From a macroscopically point of view, it is import
A Wright function based framework is proposed to combine and extend several distribution families. The $α$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution family subsumes those of the original $α$-stable, Student’s t distribu
Combining model-based and model-free reinforcement learning approaches, this paper proposes and analyzes an $ε$-policy gradient algorithm for the online pricing learning task. The algorithm extends $ε$-greedy algorithm by replacing greedy exploitation with gradient descent step and facilitates learn
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to reduce variance, as earlier proposed by Kebaier (2005). We in
This paper introduces an approach to reference class selection in distributional forecasting with an application to corporate sales growth rates using several co-variates as reference variables, that are implicit predictors. The method can be used to detect expert or model-based forecasts exposed to
In this paper, we introduce a suite of models for price-aware automated market making platforms willing to optimize their quotes. These models incorporate advanced price dynamics, including stochastic volatility, jumps, and microstructural price models based on Hawkes processes. Additionally, we add
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a rigorous analysis of hedge errors within the Black-Scholes fram
Exploring complex adaptive financial trading environments through multi-agent based simulation methods presents an innovative approach within the realm of quantitative finance. Despite the dominance of multi-agent reinforcement learning approaches in financial markets with observable data, there exi