Multi-Asset / Equities

Solving dynamic portfolio selection problems via score-based diffusion models ArXiv ID: 2507.09916 “View on arXiv” Authors: Ahmad Aghapour, Erhan Bayraktar, Fengyi Yuan Abstract 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 which we can easily and adequately sample). With adaptive training and sampling methods that are tailor-made for time series data, we obtain quantification bounds between $\mathbb P$ and $\mathbb Q$ in terms of the adapted Wasserstein metric $\mathcal A W_2$. Importantly, the proposed adapted sampling method also facilitates {"\it conditional sampling"}. In the second part of this paper, we provide the stability of the mean-variance portfolio optimization problems in $\mathcal A W _2$. Then, combined with the error bounds and the stability result, we propose a policy gradient algorithm based on the generative environment, in which our innovative adapted sampling method provides approximate scenario generators. We illustrate the performance of our algorithm on both simulated and real data. For real data, the algorithm based on the generative environment produces portfolios that beat several important baselines, including the Markowitz portfolio, the equal weight (naive) portfolio, and S&P 500. ...

Dynamic Black-Litterman ArXiv ID: 2404.18822 “View on arXiv” Authors: Unknown Abstract The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the investor. We consider a generalization where the investor trades dynamically and views can be over horizons that differ from the investor. By exploiting the underlying graphical structure relating the asset prices and views, we derive the conditional distribution of asset returns when the price process is geometric Brownian motion, and show that it can be written in terms of a multi-dimensional Brownian bridge. The components of the Brownian bridge are dependent one-dimensional Brownian bridges with hitting times that are determined by the statistics of the price process and views. The new price process is an affine factor model with the conditional log-price process playing the role of a vector of factors. We derive an explicit expression for the optimal dynamic investment policy and analyze the hedging demand for changes in the new covariate. More generally, the paper shows that Bayesian graphical models are a natural framework for incorporating complex information structures in the Black-Litterman model. The connection between Brownian motion conditional on noisy observations of its terminal value and multi-dimensional Brownian bridge is novel and of independent interest. ...

Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors ArXiv ID: ssrn-925138 “View on arXiv” Authors: Unknown Abstract In sharp contrast to the recommendations of Modern Portfolio Theory (MPT), a vast majority of investors are not well diversified. This neglect of diversificatio Keywords: portfolio diversification, modern portfolio theory, asset allocation, investor behavior, risk management, Multi-Asset / Equities Complexity vs Empirical Score Math Complexity: 3.0/10 Empirical Rigor: 2.0/10 Quadrant: Philosophers Why: The paper proposes a conceptual framework extending Markowitz by adding personal and aspirational risk dimensions, relying on qualitative discussion and examples rather than dense mathematical derivations or rigorous backtesting. flowchart TD R["Research Goal: Why do investors fail to diversify despite MPT?"] --> M["Methodology: Qualitative Analysis of Investor Behavior"] M --> D["Data Inputs: Empirical Data & Behavioral Observations"] D --> C["Computational Process: Multi-Asset Portfolio Simulation"] C --> F["Key Findings: Investors prioritize simplicity and familiarity over theoretical optimal allocation"] F --> O["Outcome: Proposed Comprehensive Wealth Allocation Framework"]