Optimization Methods

In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals

Data scarcity and confidentiality in finance often impede model development and robust testing. This paper presents a unified multi-criteria evaluation framework for synthetic financial data and applies it to three representative generative paradigms: the statistical ARIMA-GARCH baseline, Variationa

Conditional Autoencoders (CAEs) offer a flexible, interpretable approach for estimating latent asset-pricing factors from firm characteristics. However, existing studies usually limit the latent factor dimension to around K=5 due to concerns that larger K can degrade performance. To overcome this ch

This study introduces a portfolio optimization framework to minimize mixed conditional value at risk (MCVaR), incorporating a chance constraint on expected returns and limiting the number of assets via cardinality constraints. A robust MCVaR model is presented, which presumes ellipsoidal support for

This study presents a Reinforcement Learning (RL)-based portfolio management model tailored for high-risk environments, addressing the limitations of traditional RL models and exploiting market opportunities through two-sided transactions and lending. Our approach integrates a new environmental form

We study the construction and rebalancing of sparse index-tracking portfolios from an operational research perspective, with explicit emphasis on uncertainty quantification and implementability. The decision variables are portfolio weights constrained to sum to one; the aims are to track a reference

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

Classical portfolio models tend to degrade under structural breaks, whereas flexible machine-learning allocators often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that links structural causal drivers, nonlinear filtering, and forward-bac

In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we parameterise trading strategies as functions in a reproducing kernel

This paper presents a comprehensive machine learning framework for quantitative trading that achieves superior risk-adjusted returns through systematic factor engineering, real-time computation optimization, and cross-sectional portfolio construction. Our approach integrates multi-factor alpha disco

Expectiles are the only law-invariant risk measures that are both coherent and elicitable. Unlike Conditional Value-at-Risk (CVaR), however, they do not admit a Rockafellar–Uryasev representation that admits tractable Wasserstein reformulations. We address this difficulty by developing an envelope

HFT systems are conventionally built as a single-threaded event loop, on the rule that every thread hop adds latency. We test that rule against a measurement study of more than a year of CME market data for the NQ front-month contract, following every packet and matching-engine transaction through t

Cross-market portfolio optimization has become increasingly complex with the globalization of financial markets and the growth of high-frequency, multi-dimensional datasets. Traditional artificial neural networks, while effective in certain portfolio management tasks, often incur substantial computa

Portfolio optimization constitutes a cornerstone of risk management by quantifying the risk-return trade-off. Since it inherently depends on accurate parameter estimation under conditions of future uncertainty, the selection of appropriate input parameters is critical for effective portfolio constru

Maximizing revenue for grid-scale battery energy storage systems in continuous intraday electricity markets requires strategies that are able to seize trading opportunities as soon as new information arrives. This paper introduces and evaluates an automated high-frequency trading strategy for batter

Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than 5) parameters which can be calibrated to market data. A more

We formulate option market making as a constrained, risk-sensitive control problem that unifies execution, hedging, and arbitrage-free implied-volatility surfaces inside a single learning loop. A fully differentiable eSSVI layer enforces static no-arbitrage conditions (butterfly and calendar) while

We study portfolio choice when firm-level emissions intensities are measured with error. We introduce a scope-specific penalty operator that rescales asset payoffs as a smooth function of revenue-normalized emissions intensity. Under payoff homogeneity, unit-scale invariance, mixture linearity, and

Forecasting accuracy is routinely optimised in financial prediction tasks even though investment and risk-management decisions are executed under transaction costs, market impact, capacity limits, and binding risk constraints. This paper treats forecasting as an econometric input to a constrained de

We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or assumptions on an option pricing model, our models depart fundament

In this paper, we discuss portfolio selection strategies for Enhanced Indexation (EI), which are based on stochastic dominance relations. The goal is to select portfolios that stochastically dominate a given benchmark but that, at the same time, must generate some excess return with respect to a ben

Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the allocated capital captures the diversification benefit of the margi

Large-scale portfolio choice is highly sensitive to estimation error, making the preliminary asset selection essential in empirical implementation. Existing selection rules typically rely on scalar returns or low dimensional high frequency summaries, and thus discard intraday risk dynamics that may

Unrestricted mean-variance-skewness-kurtosis portfolio optimization can capture asymmetry and tail risk, but sample-moment formulations become computationally impractical when the asset universe is large: they produce dense nonconvex quartic objectives with prohibitive coskewness and cokurtosis tens

Current tokenization methods process sequential data without accounting for signal quality, limiting their effectiveness on noisy real-world corpora. We present QA-Token (Quality-Aware Tokenization), which incorporates data reliability directly into vocabulary construction. We make three key contrib

The Fundamental Review of the Trading Book (FRTB) poses a significant challenge for exotic derivatives pricing, particularly for non-modelable risk factors (NMRF) where sparse market data leads to infinite audit bounds under classical Martingale Optimal Transport (MOT). We propose a unified Rough Ma

Machine learning is central to empirical asset pricing, but portfolio construction still relies on point predictions and largely ignores asset-specific estimation uncertainty. We propose a simple change: sort assets using uncertainty-adjusted prediction bounds instead of point predictions alone. Acr

We present a high-level framework that explains why, in practice, different pricing models calibrated to the same vanilla surface tend to produce similar valuations for exotic derivatives. Our approach acts as an overlay on the Monte Carlo infrastructure already used in banks, combining path reweigh

We tackle high-dimensional, path-dependent valuation and control and introduce a deep BSDE/2BSDE solver that couples truncated log-signatures with a neural rough differential equation (RDE) backbone. The architecture aligns stochastic analysis with sequence-to-path learning: a CVaR-tilted terminal o

Transaction costs and regime shifts are major reasons why paper portfolios fail in live trading. We introduce FR-LUX (Friction-aware, Regime-conditioned Learning under eXecution costs), a reinforcement learning framework that learns after-cost trading policies and remains robust across volatility-li

Portfolio optimization is a routine asset management operation conducted in financial institutions around the world. However, under real-world constraints such as turnover limits and transaction costs, its formulation becomes a mixed-integer nonlinear program that current mixed-integer optimizers of

This paper develops a unified framework that integrates behavioral distortions into rational portfolio optimization by extracting implied probability weighting functions (PWFs) from optimal portfolios modeled under Gaussian and Normal-Inverse-Gaussian (NIG) return distributions. Using DJIA constitue

Financial markets are noisy yet contain a latent graph-theoretic structure that can be exploited for superior risk-adjusted returns. We propose a quantum stochastic walk (QSW) optimizer that embeds assets in a weighted graph: nodes represent securities while edges encode the return-covariance kernel

We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and how to regularise both the eigenvalues and the marginal volatilities of large equity covariance matrices. This explicit mathematical mapp

This research systematically develops and evaluates various hybrid modeling approaches by combining traditional econometric models (ARIMA and ARFIMA models) with machine learning and deep learning techniques (SVM, XGBoost, and LSTM models) to forecast financial time series. The empirical analysis is

We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications. We apply it to an extens

This paper focuses on the developing of high-dimensional risk models to construct portfolios of securities in the US stock exchange. Investors seek to gain the highest profits and lowest risk in capital markets. We have developed various risk models and for each model different investment strategies

When it comes to stock returns, any form of predictability can bolster risk-adjusted profitability. We develop a collaborative machine learning algorithm that optimizes portfolio weights so that the resulting synthetic security is maximally predictable. Precisely, we introduce MACE, a multivariate e

Algorithmic trading relies on machine learning models to make trading decisions. Despite strong in-sample performance, these models often degrade when confronted with evolving real-world market regimes, which can shift dramatically due to macroeconomic changes-e.g., monetary policy updates or unanti

We address finance-native collateral optimization under ISDA Credit Support Annexes (CSAs), where integer lots, Schedule A haircuts, RA/MTA gating, and issuer/currency/class caps create rugged, legally bounded search spaces. We introduce a certifiable hybrid pipeline purpose-built for this domain: (

We examine whether regime-conditioned generative scenarios combined with a convex CVaR allocator improve portfolio decisions under regime shifts. We present MARCD, a generative-to-decision framework with: (i) a Gaussian HMM to infer latent regimes; (ii) a diffusion generator that produces regime-con

Financial returns are known to exhibit heavy tails, volatility clustering and abrupt jumps that are poorly captured by classical diffusion models. Advances in machine learning have enabled highly flexible functional forms for conditional means and volatilities, yet few models deliver interpretable s

We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The uncertainty is taken into account by considering the worst-case

We propose a scalable, policy-centric framework for continuous-time multi-asset portfolio-consumption optimization under inequality constraints. Our method integrates neural policies with Pontryagin’s Maximum Principle (PMP) and enforces feasibility by maximizing a log-barrier-regularized Hamiltonia

In this paper, we propose a complete modelling framework to value several batteries in the electricity intraday market at the trading session scale. The model consists of a stochastic model for the 24 mid-prices (one price per delivery hour) combined with a deterministic model for the liquidity cost

In this paper, we present a novel trading strategy that integrates reinforcement learning methods with clustering techniques for portfolio management in multi-period trading. Specifically, we leverage the clustering method to categorize stocks into various clusters based on their financial indices.

In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American options using dynamic programming, and then employing static spars

We introduce Deep Inception Networks (DINs), a family of Deep Learning models that provide a general framework for end-to-end systematic trading strategies. DINs extract time series (TS) and cross sectional (CS) features directly from daily price returns. This removes the need for handcrafted featur

We introduce an ensemble learning method based on Gaussian Process Regression (GPR) for predicting conditional expected stock returns given stock-level and macro-economic information. Our ensemble learning approach significantly reduces the computational complexity inherent in GPR inference and lend

Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion proces

Considering the continuous-time Mean-Variance (MV) portfolio optimization problem, we study a regime-switching market setting and apply reinforcement learning (RL) techniques to assist informed exploration within the control space. We introduce and solve the Exploratory Mean Variance with Regime Swi

In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can efficiently approximate the labels and their derivatives with respe

We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across

Dynamic AMM pools, as found in Temporal Function Market Making, rebalance their holdings to a new desired ratio (e.g. moving from being 50-50 between two assets to being 90-10 in favour of one of them) by introducing an arbitrage opportunity that disappears when their holdings are in line with their

In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility uncertainty. Thus the related portfolio has upper variance (maxim

This paper proposes an Extended State-Dependent Hawkes Process (ExsdHawkes) to model the intricate dynamics of Limit Order Books (LOBs). Our theoretical contribution lies in relaxing traditional constraints by allowing for state disappearances – a phenomenon frequently observed in high-frequency tr

The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control problem is high-dimensional. We propose a backward actor-critic

Metaheuristic algorithms for cardinality-constrained portfolio optimization require repair operators to map infeasible candidates onto the feasible region. Standard Euclidean projection treats assets as independent and can ignore the covariance structure that governs portfolio risk, potentially prod

We revisit Merton’s continuous-time portfolio selection through a data-driven, distributionally robust lens. Our aim is to tap the benefits of frequent trading over short horizons while acknowledging that drift is hard to pin down, whereas volatility can be screened using realized or implied measure

As renewable energy integration increases supply variability, battery energy storage systems (BESS) present a viable solution for balancing supply and demand. This paper proposes a novel approach for optimizing battery BESS participation in multiple electricity markets. We develop a joint bidding st

We propose a novel conditional diffusion model for portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on asset-specific factors. The model builds on the Diffusion Transformer with token-wise conditioning, linking each asset’s return to its own f

We propose a two-step graph learning approach for foreign exchange statistical arbitrages (FXSAs), addressing two key gaps in prior studies: the absence of graph-learning methods for foreign exchange rate prediction (FXRP) that leverage multi-currency and currency-interest rate relationships, and th

The efficiency of decentralized exchanges (DEXs) and the influence of token routing algorithms on market performance and stakeholder outcomes remain underexplored. This paper introduces the concept of Standardized Total Arbitrage Profit (STAP), computed via convex optimization, as a systematic measu

Stock recommendation is critical in Fintech applications, which use price series and alternative information to estimate future stock performance. Although deep learning models are prevalent in stock recommendation systems, traditional time-series forecasting training often fails to capture stock tr

This study proposes a novel portfolio optimization framework that integrates statistical social network analysis with time series forecasting and risk management. Using daily stock data from the S&P 500 (2020-2024), we construct dependency networks via Vector Autoregression (VAR) and Forecast Error

We develop a mathematical model for intraday dispatch of co-located wind-battery energy assets. Focusing on the primary objective of firming grid-side actual production vis-a-vis the preset day-ahead hourly generation targets, we conduct a comprehensive study of the resulting stochastic control prob

We study continuous-time mean–variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes, yet the coefficients of these processes are unknown. Based on the recently developed reinforcement learning (RL) theory for

Apart from assessing individual asset performance, investors in financial markets also need to consider how a set of firms performs collectively as a portfolio. Whereas traditional Markowitz-based mean-variance portfolios are widespread, network-based optimisation techniques offer a more flexible to

In this paper, we introduce the Dynamic Modularity-Spectral Algorithm (DynMSA), a novel approach to identify clusters of stocks with high intra-cluster correlations and low inter-cluster correlations by combining Random Matrix Theory with modularity optimisation and spectral clustering. The primary

This study focuses on building an algorithmic investment strategy employing a hybrid approach that combines LSTM and ARIMA models referred to as LSTM-ARIMA. This unique algorithm uses LSTM to produce final predictions but boosts the results of this RNN by adding the residuals obtained from ARIMA pre

We propose an approach to construct text-based time-series indices in an optimal way–typically, indices that maximize the contemporaneous relation or the predictive performance with respect to a target variable, such as inflation. We illustrate our methodology with a corpus of news articles from the

Rules are widely used in Fintech institutions to make fraud prevention decisions, since rules are highly interpretable thanks to their intuitive if-then structure. In practice, a two-stage framework of fraud prevention decision rule set mining is usually employed in large Fintech institutions; Stage

Cryptocurrency trading represents a nascent field of research, with growing adoption in industry. Aided by its decentralised nature, many metrics describing cryptocurrencies are accessible with a simple Google search and update frequently, usually at least on a daily basis. This presents a promising

In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error

Formulaic alpha discovery seeks symbolic expressions that predict cross-sectional asset returns. In deployment, multiple formulas are combined into an alpha pool, where each formula is valued through the complementary information it contributes to joint predictive performance. While Reinforcement Le

The enhanced index tracking (EIT) portfolio selection problem aims to construct a portfolio that is expected to outperform a benchmark index. In practice, investors face uncertainty in the joint distribution of asset and index losses, as the true distribution is typically unknown and only partial in

Decision-focused learning (DFL) trains predictors through downstream objectives, but a different loss need not provide an independent parameter-update direction. We characterize this restriction through the predictor Jacobian, using sparse index tracking to distinguish the covariance entries read by

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics wit

Stock price forecasting is a long-standing challenge in computational finance, driven by the inherent randomness of markets and complex temporal patterns. While recent deep-learning models have raised forecasting accuracy by jointly modeling inter-stock and temporal price dynamics, they conflate int

ESG-aware portfolio optimization is increasingly important for sustainable capital allocation, yet most learning-based methods still operationalize ESG by appending static scores to the policy observation or reward. This creates a mismatch for sequential control: ESG scores are noisy, provider-depen

Many real-world problems require sequential decisions under uncertainty: when to inject or withdraw gas from storage, how to rebalance a pension portfolio each month, what temperature profile to run through a pharmaceutical reactor chain. Dynamic programming solves small instances exactly but scales

Connectedness measures quantify aggregate risk spillovers but obscure the local interaction patterns that generate systemic risk. We develop a motif-based framework that first extracts multiscale backbones from quantile connectedness networks and then identifies directed triadic motifs whose frequen

Electricity price forecasting supports decision-making in energy markets and asset operation. Probabilistic forecasts are increasingly adopted to explicitly quantify uncertainty, typically issued as quantile predictions or ensembles of the full predictive distribution. However, how improvements in s

We study cubic cardinality-constrained portfolio optimization, a higher-order extension of the standard Markowitz formulation where three-way sector co-movement terms augment the quadratic risk-return objective. Classical heuristics like simulated annealing (SA) and tabu search require Rosenberg qua

Money-back guarantees (MBGs) are features of pooled retirement income products that address bequest concerns by ensuring the initial premium is returned through lifetime payments or, upon early death, as a death benefit to the estate. This paper studies optimal retirement decumulation in an individu

We study the problem of forecasting and optimally trading day-ahead versus real-time (DART) price spreads in U.S. wholesale electricity markets. Building on the framework of Galarneau-Vincent et al., we extend spike prediction from a single zone to a multi-zone setting and treat both positive and ne

Revisiting the continuous-time Mean-Variance (MV) Portfolio Optimization problem, we model the market dynamics with a jump-diffusion process and apply Reinforcement Learning (RL) techniques to facilitate informed exploration within the control space. We recognize the time-inconsistency of the MV pro

The integration of Deep Reinforcement Learning (DRL) and Evolutionary Computation (EC) is frequently hypothesized to be the “Holy Grail” of algorithmic trading, promising systems that adapt autonomously to non-stationary market regimes. This paper presents a rigorous post-mortem analysis of “Galaxy

This paper proposes a reinforcement learning–based framework for cryptocurrency portfolio management using the Soft Actor–Critic (SAC) and Deep Deterministic Policy Gradient (DDPG) algorithms. Traditional portfolio optimization methods often struggle to adapt to the highly volatile and nonlinear dyn

We study the dynamic investment decisions of investors who prioritise specific quantiles of outcomes over their expected values. Downside-focused agents targeting low quantiles reduce risk in states with high variance, while those with a preference for high quantiles concentrate in sleeves with high

Since the COVID-19 pandemic, the number of investors in the Indonesia Stock Exchange has steadily increased, emphasizing the importance of portfolio optimization in balancing risk and return. The classical mean-variance optimization model, while widely applied, depends on historical return and risk

Effective supply chain management under high-variance demand requires models that jointly address demand uncertainty and digital contracting adoption. Existing research often simplifies demand variability or treats adoption as an exogenous decision, limiting relevance in e-commerce and humanitarian

In volatile financial markets, balancing risk and return remains a significant challenge. Traditional approaches often focus solely on equity allocation, overlooking the strategic advantages of options trading for dynamic risk hedging. This work presents DeltaHedge, a multi-agent framework that inte

This paper proposes a reinforcement learning framework that employs Proximal Policy Optimization (PPO) to dynamically optimize the weights of multiple large language model (LLM)-generated formulaic alphas for stock trading strategies. Formulaic alphas are mathematically defined trading signals deriv

This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the

The efficient and effective construction of portfolios that adhere to real-world constraints is a challenging optimization task in finance. We investigate a concrete representation of the problem with a focus on design proposals of an Exchange Traded Fund. We evaluate the sampling-based CVaR Variati

This paper presents a novel hierarchical framework for portfolio optimization, integrating lightweight Large Language Models (LLMs) with Deep Reinforcement Learning (DRL) to combine sentiment signals from financial news with traditional market indicators. Our three-tier architecture employs base RL

Recent advances in deep learning have spurred the development of end-to-end frameworks for portfolio optimization that utilize implicit layers. However, many such implementations are highly sensitive to neural network initialization, undermining performance consistency. This research introduces a ro

Existing black-box portfolio management systems are prevalent in the financial industry due to commercial and safety constraints, though their performance can fluctuate dramatically with changing market regimes. Evaluating these non-transparent systems is computationally expensive, as fixed budgets

This study introduces a dynamic investment framework to enhance portfolio management in volatile markets, offering clear advantages over traditional static strategies. Evaluates four conventional approaches : equal weighted, minimum variance, maximum diversification, and equal risk contribution unde