Execution algorithms are vital to modern trading, they enable market participants to execute large orders while minimising market impact and transaction costs. As these algorithms grow more sophisticated, optimising them becomes increasingly challenging. In this work, we present a reinforcement learning (RL) framework for discovering optimal execution strategies, evaluated within a reactive agent-based market simulator. This simulator creates reactive order flow and allows us to decompose slippage into its constituent components: market impact and execution risk. We assess the RL agent's performance using the efficient frontier based on work by Almgren and Chriss, measuring its ability to balance risk and cost. Results show that the RL-derived strategies consistently outperform baselines and operate near the efficient frontier, demonstrating a strong ability to optimise for risk and impact. These findings highlight the potential of reinforcement learning as a powerful tool in the trader's toolkit.

MOPBnB(so) evaluates a noisy function exactly once at any solution and uses neighboring solutions to estimate the objective functions, in contrast to a variant that uses multiple replications at a solution to estimate the objective functions. A finite-time performance analysis for deterministic multi-objective problems provides a bound on the probability that MOPBnB(so) captures the Pareto optimal set. Asymptotic convergence of MOPBnB(so) on stochastic problems is derived, in that the algorithm captures the Pareto optimal set and the estimations converge to the true objective function values. Numerical results reveal that the variant with multiple replications is extremely intensive in terms of computational resources compared to MOPBnB(so). In addition, numerical results show that MOPBnB(so) outperforms a genetic algorithm NSGA-II on test problems. Keywords: global optimization; multiple objectives; branch and bound; stochastic optimization; estimation 1 Introduction Multiple objectives generally exist for practical problems, and providing solutions to multi-objective problems is more challenging than for single objective problems (Miettinen, 2012).

Machine learning (ML) techniques have become ubiquitous in the financial industry due to their powerful predictive performance. However, ML model outputs may lead to certain types of unintended bias, which are measures of unfairness that impact protected sub-populations. Predictive models, and strategies that rely on such models, are subject to laws and regulations that ensure fairness. For instance, financial institutions (FIs) in the U.S. that are in the business of extending credit to applicants are subject to the Equal Credit Opportunity Act (ECOA) [14] and the Fair Housing Act (FHA) [13], which prohibit discrimination in credit offerings and housing transactions. The protected classes identified in the laws, including race, gender, age (subject to very limited exceptions), ethnicity, national origin, and material status, cannot be used as attributes in lending decisions.

Estimating the mean-variance efficient (MVE) frontier is crucial for asset pricing and investment management. Yet, estimating the tangency portfolio (Markowitz, 1952) using the unbalanced panel of thousands of individual asset returns proves impracticable. Empirical studies typically consider a "diversified" set of test assets (e.g., ME-BM 25 portfolios) to estimate and evaluate factor models, hoping these test assets or a few common factors can span the same efficient frontier as individual assets. However, popular factor models hardly explain the cross section of conventional prespecified test assets (e.g., Kozak et al., 2018; Lopez-Lira and Roussanov, 2020), not to mention the ad hoc nature of these test assets hampers the effectiveness of model estimations and evaluations (Lewellen et al., 2010; Ang et al., 2020). For example, characteristics-based test assets are often limited to univariate-and bivariate-sorted portfolios due to the challenges of high-dimensional sorting (Cochrane, 2011), overlooking nonlinearity and asymmetric interactions (that do not uniformly apply to all assets), even with dependent sorting (Daniel et al., 1997).

The efficient frontier (EF) is a fundamental resource allocation problem where one has to find an optimal portfolio maximizing a reward at a given level of risk. This optimal solution is traditionally found by solving a convex optimization problem. In this paper, we introduce NeuralEF: a fast neural approximation framework that robustly forecasts the result of the EF convex optimizations problems with respect to heterogeneous linear constraints and variable number of optimization inputs. By reformulating an optimization problem as a sequence to sequence problem, we show that NeuralEF is a viable solution to accelerate large-scale simulation while handling discontinuous behavior.

For financial time series, the shortage of samples makes it statistically hard for empirical processes to achieve an acceptable confidence level in describing the underlying market distribution. In practice, it is widely recognized among financial engineers that back-testing exclusively on empirical market data results in significant over-fitting, which leads to unpredictably high risks in decision making based on these tests [Bai+16]. Synthetic data are therefore generated to augment scarce market data, and used to improve backtesting, stress-testing, exploring new scenarios, and in deep learning processes in financial applications; see the overview given in [Ass+20a]. For those purposes, the generated data should look like plausible samples from the underlying market distribution, for example reproducing stylized facts observed in the market. In particular, we want the distribution of the generated data to be close to the underlying market distribution in their performance on decision making problems, such as pricing and hedging, as well as optimal stopping and utility maximization. Notably, these problems are not continuous with respect to widely used distances, such as the Maximum Mean Discrepancy (MMD) and the Wasserstein distances (W-distances). On the other hand, these problems are Lipschitz-continuous with respect to stronger metrics, called adapted Wasserstein distances (AW-distances) [Bac+20; PP14].

Designing an optimum portfolio for allocating suitable weights to its constituent assets so that the return and risk associated with the portfolio are optimized is a computationally hard problem. The seminal work of Markowitz that attempted to solve the problem by estimating the future returns of the stocks is found to perform sub-optimally on real-world stock market data. This is because the estimation task becomes extremely challenging due to the stochastic and volatile nature of stock prices. This work illustrates three approaches to portfolio design minimizing the risk, optimizing the risk, and assigning equal weights to the stocks of a portfolio. Thirteen critical sectors listed on the National Stock Exchange (NSE) of India are first chosen. Three portfolios are designed following the above approaches choosing the top ten stocks from each sector based on their free-float market capitalization. The portfolios are designed using the historical prices of the stocks from Jan 1, 2017, to Dec 31, 2022. The portfolios are evaluated on the stock price data from Jan 1, 2022, to Dec 31, 2022. The performances of the portfolios are compared, and the portfolio yielding the higher return for each sector is identified.

In this paper, we explore potential uses of generative AI models, such as ChatGPT, for investment portfolio selection. Trusting investment advice from Generative Pre-Trained Transformer (GPT) models is a challenge due to model "hallucinations", necessitating careful verification and validation of the output. Therefore, we take an alternative approach. We use ChatGPT to obtain a universe of stocks from S&P500 market index that are potentially attractive for investing. Subsequently, we compared various portfolio optimization strategies that utilized this AI-generated trading universe, evaluating those against quantitative portfolio optimization models as well as comparing to some of the popular investment funds. Our findings indicate that ChatGPT is effective in stock selection but may not perform as well in assigning optimal weights to stocks within the portfolio. But when stocks selection by ChatGPT is combined with established portfolio optimization models, we achieve even better results. By blending strengths of AI-generated stock selection with advanced quantitative optimization techniques, we observed the potential for more robust and favorable investment outcomes, suggesting a hybrid approach for more effective and reliable investment decision-making in the future.

In this paper, a heuristic method based on TabuSearch and TokenRing Search is being used in order to solve the Portfolio Optimization Problem. The seminal mean-variance model of Markowitz is being considered with the addition of cardinality and quantity constraints to better capture the dynamics of the trading procedure, the model becomes an NP-hard problem that can not be solved using an exact method. The combination of three different neighborhood relations is being explored with Tabu Search. In addition, a new constructive method for the initial solution is proposed. Finally, I show how the proposed techniques perform on public benchmarks

Portfolio optimization is the process of choosing the best portfolio among the set of all portfolios. The naive way is to select a group of random allocations and figure out which one has the best Sharpe Ratio. This is known as the Monte Carlo Simulation where randomly a weight is assigned to each security in the portfolio and then the mean daily return and standard deviation of daily return is calculated. This helps in calculating the Sharpe Ratio for randomly selected allocations. But the naive way is time taking so an optimization algorithm is used which works on the concept of the minimizer.