It is known that the price of call options in the Heston model is determined in a non-unique way. In this paper, this problem is analyzed from the point of view of the existing mathematical theory of uniqueness classes for degenerate parabolic equations. For the special case of degeneracy, a new exa
This paper considers an insurer with two collaborating business lines that must make three critical decisions: (1) dividend payout, (2) a combination of proportional and excess-of-loss reinsurance coverage, and (3) capital injection between the lines. The reserve level of each line is modeled using
This paper presents a deep reinforcement learning (DRL) framework for dynamic portfolio optimization under market uncertainty and risk. The proposed model integrates a Sharpe ratio-based reward function with direct risk control mechanisms, including maximum drawdown and volatility constraints. Proxi
This paper introduces the Fractal-Chaotic Oscillation Co-driven (FCOC) framework, a novel paradigm for financial volatility forecasting that systematically resolves the dual challenges of feature fidelity and model responsiveness. FCOC synergizes two core innovations: our novel Fractal Feature Corre
Europe’s largest bank by assets as of 2025 started out in the 1860s in one of Europe’s colonies: The Hongkong and Shanghai Banking Co (HSBC). Multiple wars forced Qing China and later the young Republic of China into a series of unequal treaties, one of which was the forced legalisation of the opium
We enhance the Universal Portfolio Shrinkage Approximator (UPSA) of Kelly et al. (2023) by making it more robust with respect to estimation noise and covariate shift. UPSA optimizes the realized Sharpe ratio using a relatively small calibration window, leveraging ridge penalties and cross-validation
We study the construction of SPX–VIX (multi\textendash product) option surfaces that are simultaneously free of static arbitrage and dynamically chain\textendash consistent across maturities. Our method unifies \emph{“constructive”} PCA–Smolyak approximation and a \emph{“chain\textendash consistent”
In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Ma
Corporate insiders have control of material non-public preferential information (MNPI). Occasionally, the insiders strategically bypass legal and regulatory safeguards to exploit MNPI in their execution of securities trading. Due to a large volume of transactions a detection of unlawful insider trad
We revisit the optimal dividend problem of de Finetti by adding a variance term to the usual criterion of maximizing the expected discounted dividends paid until ruin, in a singular control framework. Investors do not like variability in their dividend distribution, and the mean-variance (MV) criter
We test whether simple, interpretable state variables-trend and momentum-can generate durable out-of-sample alpha in one of the world’s most liquid assets, gold. Using a rolling 10-year training and 6-month testing walk-forward from 2015 to 2025 (2,793 trading days), we convert a smoothed trend-mome
We investigate a number of Artificial Neural Network architectures (well-known and more ``exotic’’) in application to the long-term financial time-series forecasts of indexes on different global markets. The particular area of interest of this research is to examine the correlation of these indexes’
We develop a finite-horizon model in which liquid-asset returns exhibit Levy-stable scaling on a data-driven window [“tau_UV, tau_IR”] and aggregate into a finite-variance regime outside. The window and the tail index alpha are identified from the log-log slope of the central body and a two-segment
We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein distance to a reference distribution. We first examine very
We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal approximation theorem with explicit network-size bounds for
Probabilistic forecasting is crucial in multivariate financial time-series for constructing efficient portfolios that account for complex cross-sectional dependencies. In this paper, we propose Diffolio, a diffusion model designed for multivariate financial time-series forecasting and portfolio cons
We introduce a conditional Denoising Diffusion Probabilistic Model (DDPM) for generating arbitrage-free implied volatility (IV) surfaces, offering a more stable and accurate alternative to existing GAN-based approaches. To capture the path-dependent nature of volatility dynamics, our model is condit
We use a neural network to identify the optimal solution to a family of optimal investment problems, where the parameters determining an investor’s risk and consumption preferences are given as inputs to the neural network in addition to economic variables. This is used to develop a practical tool t
We propose ARBITER, a risk-neutral neural operator for learning joint SPX-VIX term structures under no-arbitrage constraints. ARBITER maps market states to an operator that outputs implied volatility and variance curves while enforcing static arbitrage (calendar, vertical, butterfly), Lipschitz boun
This paper evaluates the performance of classical time series models in forecasting Bitcoin prices, focusing on ARIMA, SARIMA, GARCH, and EGARCH. Daily price data from 2010 to 2020 were analyzed, with models trained on the first 90 percent and tested on the final 10 percent. Forecast accuracy was as