Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point ArXiv ID: 2410.05524 “View on arXiv” Authors: Unknown Abstract We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem using deep learning and duality methods. We use deep learning methods to solve the associated Hamilton-Jacobi-Bellman equation for both the primal and dual problems, and the adjoint equation arising from the stochastic maximum principle. We compare the solution of this non-concave problem to that of concavified utility, a random function depending on the benchmark, in both complete and incomplete markets. We give some numerical results for power and log utilities to show the accuracy of the suggested algorithms. ...

Financial Performance and Economic Implications of COFCO’s Strategic Acquisition of Mengniu ArXiv ID: 2410.16299 “View on arXiv” Authors: Unknown Abstract This paper examines the merger and acquisition (M&A) process between COFCO and Mengniu Dairy, exploring the motivations behind this strategic move and identifying its key aspects. By analyzing both the financial and non-financial contributions of Mengniu Dairy to COFCO, this study provides valuable insights and references for future corporate M&A activities. The theoretical significance of this research lies in its focus on the relatively underexplored area of M&A within the dairy industry, particularly in terms of M&A contributions. Using the COFCO-Mengniu case as a model, the study broadens current research perspectives by assessing the impact of M&A from financial and non-financial standpoints, enriching the body of literature on dairy industry M&As. ...

Functional Clustering of Discount Functions for Behavioral Investor Profiling ArXiv ID: 2410.16307 “View on arXiv” Authors: Unknown Abstract Classical finance models are based on the premise that investors act rationally and utilize all available information when making portfolio decisions. However, these models often fail to capture the anomalies observed in intertemporal choices and decision-making under uncertainty, particularly when accounting for individual differences in preferences and consumption patterns. Such limitations hinder traditional finance theory’s ability to address key questions like: How do personal preferences shape investment choices? What drives investor behaviour? And how do individuals select their portfolios? One prominent contribution is Pompian’s model of four Behavioral Investor Types (BITs), which links behavioural finance studies with Keirsey’s temperament theory, highlighting the role of personality in financial decision-making. Yet, traditional parametric models struggle to capture how these distinct temperaments influence intertemporal decisions, such as how individuals evaluate trade-offs between present and future outcomes. To address this gap, the present study employs Functional Data Analysis (FDA) to specifically investigate temporal discounting behaviours revealing nuanced patterns in how different temperaments perceive and manage uncertainty over time. Our findings show heterogeneity within each temperament, suggesting that investor profiles are far more diverse than previously thought. This refined classification provides deeper insights into the role of temperament in shaping intertemporal financial decisions, offering practical implications for financial advisors to better tailor strategies to individual risk preferences and decision-making styles. ...

Numerical analysis of American option pricing in a two-asset jump-diffusion model ArXiv ID: 2410.04745 “View on arXiv” Authors: Unknown Abstract This paper addresses an important gap in rigorous numerical treatments for pricing American options under correlated two-asset jump-diffusion models using the viscosity solution framework, with a particular focus on the Merton model. The pricing of these options is governed by complex two-dimensional (2-D) variational inequalities that incorporate cross-derivative terms and nonlocal integro-differential terms due to the presence of jumps. Existing numerical methods, primarily based on finite differences, often struggle with preserving monotonicity in the approximation of cross-derivatives, a key requirement for ensuring convergence to the viscosity solution. In addition, these methods face challenges in accurately discretizing 2-D jump integrals. We introduce a novel approach to effectively tackle the aforementioned variational inequalities while seamlessly handling cross-derivative terms and nonlocal integro-differential terms through an efficient and straightforward-to-implement monotone integration scheme. Within each timestep, our approach explicitly enforces the inequality constraint, resulting in a 2-D Partial Integro-Differential Equation (PIDE) to solve. Its solution is expressed as a 2-D convolution integral involving the Green’s function of the PIDE. We derive an infinite series representation of this Green’s function, where each term is non-negative and computable. This facilitates the numerical approximation of the PIDE solution through a monotone integration method. To enhance efficiency, we develop an implementation of this monotone scheme via FFTs, exploiting the Toeplitz matrix structure. The proposed method is proved to be both $\ell_{"\infty"} $-stable and consistent in the viscosity sense, ensuring its convergence to the viscosity solution of the variational inequality. Extensive numerical results validate the effectiveness and robustness of our approach. ...

Optimal execution with deterministically time varying liquidity: well posedness and price manipulation ArXiv ID: 2410.04867 “View on arXiv” Authors: Unknown Abstract We investigate the well-posedness in the Hadamard sense and the absence of price manipulation in the optimal execution problem within the Almgren-Chriss framework, where the temporary and permanent impact parameters vary deterministically over time. We present sufficient conditions for the existence of a unique solution and provide second-order conditions for the problem, with a particular focus on scenarios where impact parameters change monotonically over time. Additionally, we establish conditions to prevent transaction-triggered price manipulation in the optimal solution, i.e. the occurence of buying and selling in the same trading program. Our findings are supported by numerical analyses that explore various regimes in simple parametric settings for the dynamics of impact parameters. ...

Temporal Relational Reasoning of Large Language Models for Detecting Stock Portfolio Crashes ArXiv ID: 2410.17266 “View on arXiv” Authors: Unknown Abstract Stock portfolios are often exposed to rare consequential events (e.g., 2007 global financial crisis, 2020 COVID-19 stock market crash), as they do not have enough historical information to learn from. Large Language Models (LLMs) now present a possible tool to tackle this problem, as they can generalize across their large corpus of training data and perform zero-shot reasoning on new events, allowing them to detect possible portfolio crash events without requiring specific training data. However, detecting portfolio crashes is a complex problem that requires more than reasoning abilities. Investors need to dynamically process the impact of each new piece of information found in news articles, analyze the relational network of impacts across different events and portfolio stocks, as well as understand the temporal context between impacts across time-steps, in order to obtain the aggregated impact on the target portfolio. In this work, we propose an algorithmic framework named Temporal Relational Reasoning (TRR). It seeks to emulate the spectrum of human cognitive capabilities used for complex problem-solving, which include brainstorming, memory, attention and reasoning. Through extensive experiments, we show that TRR is able to outperform state-of-the-art techniques on detecting stock portfolio crashes, and demonstrate how each of the proposed components help to contribute to its performance through an ablation study. Additionally, we further explore the possible applications of TRR by extending it to other related complex problems, such as the detection of possible global crisis events in Macroeconomics. ...

The Fourier Cosine Method for Discrete Probability Distributions ArXiv ID: 2410.04487 “View on arXiv” Authors: Unknown Abstract We provide a rigorous convergence proof demonstrating that the well-known semi-analytical Fourier cosine (COS) formula for the inverse Fourier transform of continuous probability distributions can be extended to discrete probability distributions, with the help of spectral filters. We establish general convergence rates for these filters and further show that several classical spectral filters achieve convergence rates one order faster than previously recognized in the literature on the Gibbs phenomenon. Our numerical experiments corroborate the theoretical convergence results. Additionally, we illustrate the computational speed and accuracy of the discrete COS method with applications in computational statistics and quantitative finance. The theoretical and numerical results highlight the method’s potential for solving problems involving discrete distributions, particularly when the characteristic function is known, allowing the discrete Fourier transform (DFT) to be bypassed. ...

Two-fund separation under hyperbolically distributed returns and concave utility functions ArXiv ID: 2410.04459 “View on arXiv” Authors: Unknown Abstract Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore, analytical expressions for optimal portfolios are always preferred. In our work, we study portfolio optimization problems under the expected utility criterion for a wide range of utility functions, assuming return vectors follow hyperbolic distributions. Our main result demonstrates that under this setup, the two-fund monetary separation holds. Specifically, an individual with any utility function from this broad class will always choose to hold the same portfolio of risky assets, only adjusting the mix between this portfolio and a riskless asset based on their initial wealth and the specific utility function used for decision making. We provide explicit expressions for this mutual fund of risky assets. As a result, in our economic model, an individual’s optimal portfolio is expressed in closed form as a linear combination of the riskless asset and the mutual fund of risky assets. Additionally, we discuss expected utility maximization problems under exponential utility functions over any domain of the portfolio set. In this part of our work, we show that the optimal portfolio in any given convex domain of the portfolio set either lies on the boundary of the domain or is the unique globally optimal portfolio within the entire domain. ...

Improving Portfolio Optimization Results with Bandit Networks ArXiv ID: 2410.04217 “View on arXiv” Authors: Unknown Abstract In Reinforcement Learning (RL), multi-armed Bandit (MAB) problems have found applications across diverse domains such as recommender systems, healthcare, and finance. Traditional MAB algorithms typically assume stationary reward distributions, which limits their effectiveness in real-world scenarios characterized by non-stationary dynamics. This paper addresses this limitation by introducing and evaluating novel Bandit algorithms designed for non-stationary environments. First, we present the Adaptive Discounted Thompson Sampling (ADTS) algorithm, which enhances adaptability through relaxed discounting and sliding window mechanisms to better respond to changes in reward distributions. We then extend this approach to the Portfolio Optimization problem by introducing the Combinatorial Adaptive Discounted Thompson Sampling (CADTS) algorithm, which addresses computational challenges within Combinatorial Bandits and improves dynamic asset allocation. Additionally, we propose a novel architecture called Bandit Networks, which integrates the outputs of ADTS and CADTS, thereby mitigating computational limitations in stock selection. Through extensive experiments using real financial market data, we demonstrate the potential of these algorithms and architectures in adapting to dynamic environments and optimizing decision-making processes. For instance, the proposed bandit network instances present superior performance when compared to classic portfolio optimization approaches, such as capital asset pricing model, equal weights, risk parity, and Markovitz, with the best network presenting an out-of-sample Sharpe Ratio 20% higher than the best performing classical model. ...

A Dynamic Approach to Stock Price Prediction: Comparing RNN and Mixture of Experts Models Across Different Volatility Profiles ArXiv ID: 2410.07234 “View on arXiv” Authors: Unknown Abstract This study evaluates the effectiveness of a Mixture of Experts (MoE) model for stock price prediction by comparing it to a Recurrent Neural Network (RNN) and a linear regression model. The MoE framework combines an RNN for volatile stocks and a linear model for stable stocks, dynamically adjusting the weight of each model through a gating network. Results indicate that the MoE approach significantly improves predictive accuracy across different volatility profiles. The RNN effectively captures non-linear patterns for volatile companies but tends to overfit stable data, whereas the linear model performs well for predictable trends. The MoE model’s adaptability allows it to outperform each individual model, reducing errors such as Mean Squared Error (MSE) and Mean Absolute Error (MAE). Future work should focus on enhancing the gating mechanism and validating the model with real-world datasets to optimize its practical applicability. ...