Optimization Methods

The dynamic portfolio construction problem requires dynamic modeling of the joint distribution of multivariate stock returns. To achieve this, we propose a dynamic generative factor model which uses random variable transformation as an implicit way of distribution modeling and relies on the Attentio

Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high sensitivity to change in input parameters. The heavy-tail characte

We present a white-box, risk-sensitive framework for jointly hedging SPX and VIX exposures under transaction costs and regime shifts. The approach couples an arbitrage-free market teacher with a control layer that enforces safety as constraints. On the market side, we integrate an SSVI-based implied

Portfolio optimization is constrained by linear assumptions and insufficient integration of multi-modal information in traditional models. This paper proposes a cross-modal BERT-driven Actor-Critic framework SBCA for multi-asset portfolio optimization to address the deficiencies of existing deep rei

This paper proposes a machine learning assisted portfolio optimization framework designed for low data environments and regime uncertainty. We construct a teacher student learning pipeline in which a Conditional Value at Risk (CVaR) optimizer generates supervisory labels, and neural models (Bayesian

There is emerging evidence that trust-region (TR) algorithms are very effective at solving derivative-free nonconvex stochastic optimization problems in which the objective function is a Monte Carlo (MC) estimate. A recent strand of methodologies adaptively adjusts the sample size of the MC estimate

We address the problem of executing large client orders in continuous double-auction markets under time and liquidity constraints. We propose a model predictive control (MPC) framework that balances three competing objectives: order completion, market impact, and opportunity cost. Our algorithm is g

In the context of containment of default contagion in financial networks, we here study a regulator that allocates pre-shock capital or liquidity buffers across banks connected by interbank liabilities and common external asset exposures. The regulator chooses a nonnegative buffer vector under a lin

We introduce a new agentic artificial intelligence (AI) platform for portfolio management. Our architecture consists of three layers. First, two large language model (LLM) agents are assigned specialized tasks: one agent screens for firms with desirable fundamentals, while a sentiment analysis agent

This paper proposes a machine learning-based framework for asset selection and portfolio construction, termed the Best-Path Algorithm Sparse Graphical Model (BPASGM). The method extends the Best-Path Algorithm (BPA) by mapping linear and non-linear dependencies among a large set of financial assets

Integrating hard constraints into deep learning is essential for safety-critical systems. Yet existing constructive layers that project predictions onto constraint boundaries face a fundamental bottleneck: gradient saturation. By collapsing exterior points onto lower-dimensional surfaces, standard o

This paper presents a Quantum Reinforcement Learning (QRL) solution to the dynamic portfolio optimization problem based on Variational Quantum Circuits. The implemented QRL approaches are quantum analogues of the classical neural-network-based Deep Deterministic Policy Gradient and Deep Q-Network al

Machine learning improves predictive accuracy in insurance pricing but exacerbates trade-offs between competing fairness criteria across different discrimination measures, challenging regulators and insurers to reconcile profitability with equitable outcomes. While existing fairness-aware models off

Catastrophe risk has long been recognized to pose a serious threat to the insurance sector. Catastrophe risk pooling offers an effective way to diversify losses arising from catastrophic events. In this paper, we investigate a structure of catastrophe risk pool and optimize it so that participants c

Deep hedging represents a cutting-edge approach to risk management for financial derivatives by leveraging the power of deep learning. However, existing methods often face challenges related to computational inefficiency, sensitivity to noisy data, and optimization complexity, limiting their practic

This study investigates three central questions in portfolio optimization. First, whether time-varying moment estimators outperform conventional sample estimators in practical portfolio construction. Second, whether incorporating a turnover penalty into the optimization objective can improve out-of-

The optimal control of sustainable energy supply systems, including renewable energies and energy storage, takes a central role in the decarbonization of industrial systems. However, the use of fluctuating renewable energies leads to fluctuations in energy generation and requires a suitable control

Markowitz’s optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random matrix theory, several schemes have been developed to “clean” th

The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, t

We build a balance sheet-based model to capture run risk, i.e., a reduced potential to raise capital from liquidity buffers under stress, driven by depositor scrutiny and further fueled by fire sales in response to withdrawals. The setup is inspired by the Silicon Valley Bank (SVB) meltdown in March

This research proposes a novel arbitrage approach in multivariate pair trading, termed the Optimal Trading Technique (OTT). We present a method for selectively forming a “bucket” of fiat currencies anchored to cryptocurrency for monitoring and exploiting trading opportunities simultaneously. To addr

This paper contributes to the existing literature on hedging American options with Deep Reinforcement Learning (DRL). The study first investigates hyperparameter impact on hedging performance, considering learning rates, training episodes, neural network architectures, training steps, and transactio

In Statistical Arbitrage (StatArb), classical mean reversion trading strategies typically hinge on asset-pricing or PCA based models to identify the mean of a synthetic asset. Once such a (linear) model is identified, a separate mean reversion strategy is then devised to generate a trading signal. W

This paper studies a discrete-time mean-variance model based on reinforcement learning. Compared with its continuous-time counterpart in \cite{“zhou2020mv”}, the discrete-time model makes more general assumptions about the asset’s return distribution. Using entropy to measure the cost of exploration

In this work, we explore the possibility of utilizing transfer learning techniques to address the financial portfolio optimization problem. We introduce a novel concept called “transfer risk”, within the optimization framework of transfer learning. A series of numerical experiments are conducted fro

In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian Graphical Model (GGM) based methods, Shrinkage Methods, Thr

In high-dimensional time-series analysis, it is essential to have a set of key factors (namely, the style factors) that explain the change of the observed variable. For example, volatility modeling in finance relies on a set of risk factors, and climate change studies in climatology rely on a set of

Stock return prediction is fundamental to financial decision-making, yet traditional time series models fail to capture the complex interdependencies between companies in modern markets. We propose the Full-State Graph Convolutional LSTM (FS-GCLSTM), a novel temporal graph neural network that incorp

Pair trading is one of the most effective statistical arbitrage strategies which seeks a neutral profit by hedging a pair of selected assets. Existing methods generally decompose the task into two separate steps: pair selection and trading. However, the decoupling of two closely related subtasks can

In this paper, we discuss the Dutch power market, which is comprised of a day-ahead market and an intraday balancing market that operates like an auction. Due to fluctuations in power supply and demand, there is often an imbalance that leads to different prices in the two markets, providing an oppor

We present the first application of MAP-Elites, a quality-diversity algorithm, to trade execution. Rather than searching for a single optimal policy, MAP-Elites generates a diverse portfolio of regime-specialist strategies indexed by liquidity and volatility conditions. Individual specialists achiev

We propose a novel framework for risk-sensitive reinforcement learning (RSRL) that incorporates robustness against transition uncertainty. We define two distinct yet coupled risk measures: an inner risk measure addressing state and cost randomness and an outer risk measure capturing transition dynam

We study the construction of arbitrage-free option price surfaces from noisy bid-ask quotes across strike and maturity. Our starting point is a Chebyshev representation of the call price surface on a warped log-moneyness/maturity rectangle, together with linear sampling and no-arbitrage operators ac

We investigate the static portfolio selection problem of S-shaped and non-concave utility maximization under first-order and second-order stochastic dominance (SD) constraints. In many S-shaped utility optimization problems, one should require a liquidation boundary to guarantee the existence of a f

In recent years, a rapid development of forecasting methods has led to an increase in the accuracy of predictions. In the literature, forecasts are typically evaluated using metrics such as Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). While appropriate for statistical assessment, th

This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker’s quoted prices.

This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associ

We study the problem of designing and hedging unit-linked life policies whose benefits depend on an investment fund that incorporates environmental criteria in its selection process. Offering these products poses two key challenges: constructing a green investment fund and developing a hedging strat

This paper investigates optimal investment and insurance strategies under a mean-variance criterion with path-dependent effects. We use a rough volatility model and a Hawkes process with a power kernel to capture the path dependence of the market. By adding auxiliary state variables, we degenerate a

Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration in a few securities. In this paper, we introduce novel risk m

In this paper, we tackle the dynamic mean-variance portfolio selection problem in a {"\it model-free"} manner, based on (generative) diffusion models. We propose using data sampled from the real model $\mathbb P$ (which is unknown) with limited size to train a generative model $\mathbb Q$ (from whic

We propose a profitable trading strategy for the cryptocurrency market based on grid trading. Starting with an analysis of the expected value of the traditional grid strategy, we show that under simple assumptions, its expected return is essentially zero. We then introduce a novel Dynamic Grid-based

Portfolio optimization requires dynamic allocation of funds by balancing the risk and return tradeoff under dynamic market conditions. With the recent advancements in AI, Deep Reinforcement Learning (DRL) has gained prominence in providing adaptive and scalable strategies for portfolio optimization.

Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and simultaneous perturbation stochastic approximation (SPSA), t

In this paper, we propose an efficient implementation of deep policy gradient method (PGM) for optimal control problems in continuous time. The proposed method has the ability to manage the allocation of computational resources, number of trajectories, and complexity of architecture of the neural ne

Bertsimas and Lo’s seminal work laid the groundwork for addressing the implementation shortfall dilemma in institutional investing, emphasizing the significance of market microstructure and price dynamics in minimizing execution costs. However, the ability to derive a theoretical Optimum market orde

We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations are based on random matrices, free probability, deterministic

Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero transaction costs, perfect liquidity, and continuous-time hedging

Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive optimal portfolios is energy-intensive for digital computers. W

This paper introduces a novel approach to optimizing portfolio rebalancing by integrating Graph Neural Networks (GNNs) for predicting transaction costs and Dijkstra’s algorithm for identifying cost-efficient rebalancing paths. Using historical stock data from prominent technology firms, the GNN is t

The expected regret and target semi-variance are two of the most important risk measures for downside risk. When the distribution of a loss is uncertain, and only partial information of the loss is known, their worst-case values play important roles in robust risk management for finance, insurance,

In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$ tend to infinity simultaneously and their ratio $p/n$ tends to

This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and analyzed to evaluate its effectiveness in pricing options. For p

In hedge funds, convex compensation schemes are adopted to stimulate a high-profit performance for portfolio managers. In economics, non-monotone risk aversion is proposed to argue that individuals may not be risk-averse when the wealth level is low. Combining these two ingredients, we study the opt

Martingale optimal transport (MOT) often yields broad price bounds for options, constraining their practical applicability. In this study, we extend MOT by incorporating causality constraints among assets, inspired by the nonanticipativity condition of stochastic processes. This, however, introduces

Sustainable Investing identifies the approach of investors whose aim is twofold: on the one hand, they want to achieve the best compromise between portfolio risk and return, but they also want to take into account the sustainability of their investment, assessed through some Environmental, Social, a

We propose an optimal iterative scheme for federated transfer learning, where a central planner has access to datasets ${"\cal D"}1,\dots,{"\cal D"}N$ for the same learning model $f_θ$. Our objective is to minimize the cumulative deviation of the generated parameters ${“θ_i(t)"}{“t=0”}^T$ across all

This papers proposes a generic, high-level methodology for generating forecast combinations that would deliver the optimal linearly combined forecast in terms of the mean-squared forecast error if one had access to two population quantities: the mean vector and the covariance matrix of the vector of

Agent-based models (ABMs) are a promising approach to modelling and reasoning about complex systems, yet their application in practice is impeded by their complexity, discrete nature, and the difficulty of performing parameter inference and optimisation tasks. This in turn has sparked interest in th

This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about the risk premia, the volatilities, and the correlation. The i

This work aims to deal with the optimal allocation instability problem of Markowitz’s modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT) and the machine learning allocation methodology known as Ne

In this paper, we revisit the relationship between investors’ utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(μ,σ,κ)$ returns and compare them with the mean-variance approach, which is based on Gaussian returns. We reveal

In this paper, we address the problem of probabilistic forecasting using an adaptive volatility method rooted in classical time-varying volatility models and leveraging online stochastic optimization algorithms. These principles were successfully applied in the M6 forecasting competition under the t

Battery energy storage systems (BESS) participating in multi-market electricity trading require price forecasts to optimize dispatch decisions. A widely held assumption is that forecast accuracy, measured by standard metrics such as mean absolute error (MAE), drives trading performance. We challenge

LLM agents are promising tools for empirical discovery, but their flexibility can also turn discovery into uncontrolled search. We study how to use agents under a reproducible protocol through cryptocurrency factor discovery. Our framework casts the task as sequential hypothesis search: an agent rea

Various financial market scenarios may cause heterogeneous risk assessments among analysts, which motivates the usage of the Generalized Risk Measure in Fadina et al. (2024, Finance and Stochastics). Effectively synthesizing these diverse assessments avoids over-relying on a single, potentially flaw

We present a large scale benchmark of modern deep learning architectures for a financial time series prediction and position sizing task, with a primary focus on Sharpe ratio optimization. Evaluating linear models, recurrent networks, transformer based architectures, state space models, and recent s

We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as a smooth generalization of the widely-known linear interpol

In Aarab (2020), I examine U.S. stock return predictability across economic regimes and document evidence of time-varying expected returns across market states in the long run. The analysis introduces a state-switching specification in which the market state is proxied by the slope of the yield curv

Modern high-frequency trading (HFT) environments are characterized by sudden price spikes that present both risk and opportunity, but conventional financial models often fail to capture the required fine temporal structure. Spiking Neural Networks (SNNs) offer a biologically inspired framework well-

Quantitative trading strategies rely on accurately ranking stocks to identify profitable investments. Effective portfolio management requires models that can reliably order future stock returns. Transformer models are promising for understanding financial time series, but how different training loss

In the ever-changing and intricate landscape of financial markets, portfolio optimisation remains a formidable challenge for investors and asset managers. Conventional methods often struggle to capture the complex dynamics of market behaviour and align with diverse investor preferences. To address t

In this review, we provide practical guidance on some of the main machine learning tools used in portfolio weight formation. This is not an exhaustive list, but a fraction of the ones used and have some statistical analysis behind it. All this research is essentially tied to precision matrix of exce

The rapid growth of crypto markets has opened new opportunities for investors, but at the same time exposed them to high volatility. To address the challenge of managing dynamic portfolios in such an environment, this paper presents a practical application of a multi-agent system designed to autonom

This paper introduces a novel agent-based approach for enhancing existing portfolio strategies using Proximal Policy Optimization (PPO). Rather than focusing solely on traditional portfolio construction, our approach aims to improve an already high-performing strategy through dynamic rebalancing dri

In this study, we applied the NEAT (NeuroEvolution of Augmenting Topologies) algorithm to stock trading using multiple technical indicators. Our approach focused on maximizing earning, avoiding risk, and outperforming the Buy & Hold strategy. We used progressive training data and a multi-objective f

We develop a novel two-layer approach for optimising mortgage relief products through a simulated multi-agent mortgage environment. While the approach is generic, here the environment is calibrated to the US mortgage market based on publicly available census data and regulatory guidelines. Through t

The paper employs advanced mathematical techniques including mean-variance and mean-semivariance optimization, genetic algorithms, and handles integer constraints and transaction costs. It also provides empirical analysis with simulated data, visualizations of efficient frontiers, and includes R cod

Random delays between the occurrence of accident events and the corresponding reporting times of insurance claims is a standard feature of insurance data. The time lag between the reporting and the processing of a claim depends on whether the claim can be processed without delay as it arrives or whe

This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or short positions on options. Utilizing SPY options data reco

We study the continuous-time pre-commitment mean-variance portfolio selection in a time-varying financial market. By introducing two indexes which respectively express the average profitability of the risky asset (AP) and the current profitability of the risky asset (CP), the optimal portfolio selec

In portfolio optimization, decision makers face difficulties from uncertainties inherent in real-world scenarios. These uncertainties significantly influence portfolio outcomes in both classical and multi-objective Markowitz models. To address these challenges, our research explores the power of rob

Modern portfolio optimization is centered around creating a low-risk portfolio with extensive asset diversification. Following the seminal work of Markowitz, optimal asset allocation can be computed using a constrained optimization model based on empirical covariance. However, covariance is typicall

We propose a distributional framework for benchmarking socio-technical risks of foundation models with quantified statistical significance. Our approach hinges on a new statistical relative testing based on first and second order stochastic dominance of real random variables. We show that the second

We study robust mean-variance optimization in multiperiod portfolio selection by allowing the true probability measure to be inside a Wasserstein ball centered at the empirical probability measure. Given the confidence level, the radius of the Wasserstein ball is determined by the empirical data. Th

Motivated by the current global high inflation scenario, we aim to discover a dynamic multi-period allocation strategy to optimally outperform a passive benchmark while adhering to a bounded leverage limit. To this end, we formulate an optimal control problem to outperform a benchmark portfolio thro

The aim of this paper is to investigate the impact of rebalancing frequency and transaction costs on the log-optimal portfolio, which is a portfolio that maximizes the expected logarithmic growth rate of an investor’s wealth. We prove that the frequency-dependent log-optimal portfolio problem with c

Stochastic Gradient Descent Langevin Dynamics (SGLD) algorithms, which add noise to the classic gradient descent, are known to improve the training of neural networks in some cases where the neural network is very deep. In this paper we study the possibilities of training acceleration for the numeri

Designing an intelligent volume-weighted average price (VWAP) strategy is a critical concern for brokers, since traditional rule-based strategies are relatively static that cannot achieve a lower transaction cost in a dynamic market. Many studies have tried to minimize the cost via reinforcement lea

Modern stochastic optimization pipelines increasingly rely on learned generative models to represent uncertainty, while downstream decisions are evaluated almost entirely through Monte Carlo scenarios. This shifts the operational object of uncertainty from an explicit probability law to the sampler

We present an approximate dynamic programming framework for designing degradation-aware market participation policies for battery energy storage systems. The approach employs a tailored value function approximation that reduces the state space to state of charge and battery health, while performing

We present a hybrid classical-quantum framework for portfolio construction and rebalancing. Asset selection is performed using Ledoit-Wolf shrinkage covariance estimation combined with hierarchical correlation clustering to extract n = 10 decorrelated stocks from the S&P 500 universe without survivo

Genetic Programming yields interpretable programs, but small syntactic mutations can induce large, unpredictable behavioral shifts, degrading locality and sample efficiency. We frame this as an operator-design problem: learn a continuous program space where latent distance has behavioral meaning, th

Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a comprehensive overview of the various modeling approaches and

This article proposes a unified framework for portfolio optimization (PO), recognizing an object called the `gain probability density function (PDF)’ as the fundamental object of the problem from which any objective function could be derived. The gain PDF has the advantage of being 1-dimensional for

Energy storage promotes the integration of renewables by operating with charge and discharge policies that balance an intermittent power supply. A key challenge in this emerging sector is how to optimize the operation of storage assets given future price uncertainties and the need to recover the cos

This study develops an inverse portfolio optimization framework for recovering latent investor preferences including risk aversion, transaction cost sensitivity, and ESG orientation from observed portfolio allocations. Using controlled synthetic data, we assess the estimator’s statistical properties

We propose DeepAries , a novel deep reinforcement learning framework for dynamic portfolio management that jointly optimizes the timing and allocation of rebalancing decisions. Unlike prior reinforcement learning methods that employ fixed rebalancing intervals regardless of market conditions, DeepAr

Deep Learning is evolving fast and integrates into various domains. Finance is a challenging field for deep learning, especially in the case of interpretable artificial intelligence (AI). Although classical approaches perform very well with natural language processing, computer vision, and forecasti

Sparse portfolio optimization is a fundamental yet challenging problem in quantitative finance, since traditional approaches heavily relying on historical return statistics and static objectives can hardly adapt to dynamic market regimes. To address this issue, we propose Evolutionary Factor Search