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We propose a two-level, learning-based portfolio method (RL-BHRP) that spreads risk across sectors and stocks, and adjusts exposures as market conditions change. Using U.S. Equities from 2012 to mid-2025, we design the model using 2012 to…
We propose a unified multi-tasking framework to represent the complex and uncertain causal process of financial market dynamics, and then to predict the movement of any type of index with an application on the monthly direction of the…
The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing…
Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
Over the past 60 years, there has been a gradual increase in the volatility of daily returns for the S&P 500 Index. Hypothetically, suppose that market forces determine daily volatility such that a daily leveraged S&P 500 fund cannot…
Parametric portfolio policies may experience estimation risk. I develop a generalized Bayesian framework that updates priors, delivering a posterior distribution over characteristic tilts and out-of-sample returns that is the unique…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…
We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
We analyze a negative-parameter variant of the diversity-weighted portfolio studied by Fernholz, Karatzas, and Kardaras (Finance Stoch 9(1):1-27, 2005), which invests in each company a fraction of wealth inversely proportional to the…
This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation…
This paper analyzes how expectations of Transformative AI (TAI) affect current economic behavior by introducing a novel mechanism where automation redirects labor income from workers to those controlling AI systems, with the share of…
Financial markets are interconnected, with micro-currents propagating across global markets and shaping economic trends. This paper moves beyond traditional stock market indices to examine cross-sectional return distributions-15 in our…
Attempts to allocate capital across a selection of different investments are often hampered by the fact that investors' decisions are made under limited information (no historical return data) and during an extremely limited timeframe.…
This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study's novelty is that the…
Portfolio management is essential for any investment decision. Yet, traditional methods in the literature are ill-suited for the characteristics and dynamics of cryptocurrencies. This work presents a method to build an investment portfolio…
We analyze empirical data for 4,000 real-life trading portfolios (U.S. equities) with holding periods of about 0.7-19 trading days. We find a simple scaling C ~ 1/T, where C is cents-per-share, and T is the portfolio turnover. Thus, the…
An investment portfolio consists of $n$ algorithmic trading strategies, which generate vectors of positions in trading assets. Sign opposite trades (buy/sell) cross each other as strategies are combined in a portfolio. Then portfolio…
This paper compares a series of contemporary portfolio construction approaches by employing ten U.S. stocks (TSLA, WMT, BAC, GS, LLY, MRK, GOOG, META, AAPL and XOM) in a time frame from September 2023 to December 2025. The paper explores…
This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the…