Seventy years after Markowitz, portfolio optimization is still an open problem — not because the math is unsettled, but because estimation error eats the theoretical gains. The literature here spans classical mean-variance and its regularized descendants, risk parity and volatility targeting, Black-Litterman-style view blending, and newer machine-learning approaches to covariance estimation and end-to-end allocation.
The recurring finding worth internalizing: naive equal-weight portfolios are shockingly hard to beat out of sample, so a paper’s value usually lies in how honestly it handles estimation risk — shrinkage, robust optimization, turnover penalties — rather than in the elegance of its objective function. The ranking below favors papers that test allocations on real data with realistic constraints.
Related hubs: Factor Investing & Asset Pricing, Risk Management, Machine Learning for Forecasting.
The increasing integration of data science techniques into quantitative finance has enabled more systematic and data-driven approaches to portfolio construction. This paper investigates the use of Principal Component Analysis (PCA) in constructing eigen-portfolios - portfolios derived from the princ
This paper introduces and formally verifies a novel geometric framework for first-order stochastic dominance (FSD) in $N$ dimensions using the Lean 4 theorem prover. Traditional analytical approaches to multi-dimensional stochastic dominance rely heavily on complex measure theory and multivariate ca
We prove that weak convergence within generalized gamma convolution (GGC) distributions implies convergence in the mean value. We use this fact to show the robustness of the expected utility maximizing optimal portfolio under exponential utility function when return vectors are modelled by hyperboli
We consider a rational agent who at time $0$ enters into a financial contract for which the payout is determined by a quantum measurement at some time $T>0$. The state of the quantum system is given in the Heisenberg representation by a known density matrix $\hat p$. How much will the agent be willi
This paper describes the dependence of market-based statistical moments of returns on statistical moments and correlations of the current and past trade values. We use Markowitz’s definition of value weighted return of a portfolio as the definition of market-based average return of trades during the
Investment is one of the foremost concerns of every individual investor as their small savings of today are to meet the expenses of tomorrow. Taking 200 respond
Agentic AI shifts the investor’s role from analytical execution to oversight. We present an agentic strategic asset allocation pipeline in which approximately 50 specialized agents produce capital market assumptions, construct portfolios using over 20 competing methods, and critique and vote on each
We revisit the classical Merton consumption–investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $α$-integral, interpolating between Itô, Stratonovich, and related conventions. Holding preferences and the investment opportunity s
We analyse the effect of a proportional wealth tax on asset returns, portfolio choice, and asset pricing. The tax is levied annually on the market value of all holdings at a uniform rate. We show that such a tax is economically equivalent to the government acquiring a proportional stake in the inves
We show that the Markowitz portfolio is a scalar multiple of another portfolio which replaces the covariance with the second moment matrix, via simple application of the Sherman-Morrison identity. Moreover it is shown that when using conditional estimates of the first two moments, this “Sherman-Morr
In his famous paper, Markowitz (1952) derived the dependence of portfolio random returns on the random returns of its securities. This result allowed Markowitz to obtain his famous expression for portfolio variance. We show that Markowitz’s equation for portfolio random returns and the expression fo
The Nobel-price winning Mirrlees’ theory of optimal taxation inspired a long sequence of research on its refinement and enhancement. However, an issue of concern has been always the fact that, as was shown in many publications, the optimal schedule in Mirrlees’ paradigm of maximising the total utili
In this short paper we introduce a new class of performance measures based on certainty equivalents defined via scaled utility functions. We analyse their properties, show that the corresponding portfolio optimization problem is well-posed under generic conditions, and analyse the link between portf
Machine learning (ML) is changing virtually every aspect of our lives. Today ML algorithms accomplish tasks that until recently only expert humans could perform
Myopic investors are locally rational decision-makers but globally irrational. Their suboptimal portfolios lag the market. As a consequence, other market participants are provided with profit opportunities. Not subterfuge but constrained optimisation leads to disparities. Four overlapping examples a
The passive management approach offers conservative investors a way to reduce risk concerning the market. This investment strategy aims at replicating a specific index, such as the NASDAQ Composite or the FTSE100 index. The problem is that buying all the index’s assets incurs high rebalancing costs,
This paper develops a structural framework for characterizing the informational feasibility of financial markets under heterogeneous institutional and geopolitical conditions. Departing from the assumption of uniform and time-invariant market efficiency, adaptive efficiency is conceptualized as a lo
We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton portfolio optimization problem.
Applications of Reinforcement Learning in the Finance Technology (Fintech) have acquired a lot of admiration lately. Undoubtedly Reinforcement Learning, through its vast competence and proficiency, has aided remarkable results in the field of Fintech. The objective of this systematic survey is to pe
Noted economist, Harry Markowitz (“Markowitz) received a Nobel Prize for his pioneering theoretical contributions to financial economics and corporate finance.
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