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.
This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often high-dimensional. The results demonstrate that a dynamic strat
This paper considers finitely many investors who perform mean-variance portfolio selection under relative performance criteria. That is, each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of all investors. At the inter-personal level, ea
We examine optimization problems in which an investor has the opportunity to trade in $d$ stocks with the goal of maximizing her worst-case cost of cumulative gains and losses. Here, worst-case refers to taking into account all possible drift and volatility processes for the stocks that fall within
This paper studies the mean-variance optimal portfolio choice of an investor pre-committed to a deterministic investment policy in continuous time in a market with mean-reversion in the risk-free rate and the equity risk-premium. In the tradition of Markowitz, optimal policies are restricted to a su
This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, u
We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation wh
Financial experts and analysts seek to predict the variability of financial markets. In particular, the correct prediction of this variability ensures investors successful investments. However, there has been a big trend in finance in the last years, which are the ESG criteria. Concretely, ESG (Econ
In stochastic control problems involving optimal portfolio choice, one often seeks an optimizer of some local criterion (dynamic programming value function) generated by some global criterion (e.g., expected utility). The local optimizer then typically acts as a stochastic integrand with respect to
We represent (weighted-)selection-elliptical distributions as an affine combination of the $q$ selection variables plus an elliptical term whose direction alone is independent. This form suffices for $q+2$ fund separation via first-order stochastic dominance, inter alia relaxing Simaan’s (1993) thre
A proportional wealth tax - a levy on the stock of wealth - preserves portfolio neutrality by acting as a uniform drift shift in the Fokker-Planck equation for wealth dynamics. We extend this result to the full system of ownership taxes (eierkostnader) that a shareholder faces: a corporate tax on gr
We study a goal-based portfolio selection problem in which an investor aims to meet multiple financial goals, each with a specific deadline and target amount. Trading the stock incurs a strictly positive transaction cost. Using the stochastic Perron’s method, we show that the value function is the u
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR framework has been widely explored, its time-inconsistency compl
Deep learning offers new tools for portfolio optimization. We present an end-to-end framework that directly learns portfolio weights by combining Long Short-Term Memory (LSTM) networks to model temporal patterns, Graph Attention Networks (GAT) to capture evolving inter-stock relationships, and senti
The optimal asset allocation between risky and risk-free assets is a persistent challenge due to the inherent volatility in financial markets. Conventional methods rely on strict distributional assumptions or non-additive reward ratios, which limit their robustness and applicability to investment go
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz’s Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most notably, the Markovian nature of price dynamics-that often fail t
We consider the investor who doesn’t trade shares of his portfolio. The investor only observes the current trades made in the market with his securities to estimate the current return, variance, and risks of his unchanged portfolio. We show how the time series of consecutive trades made in the marke
In this paper, we investigate mean-variance (MV) portfolio selection problems with jumps in a regime-switching financial model. The novelty of our approach lies in allowing not only the market parameters – such as the interest rate, appreciation rate, volatility, and jump intensity – to depend on th
The variance measures the portfolio risks the investors are taking. The investor, who holds his portfolio and doesn’t trade his shares, at the current time can use the time series of the market trades that were made during the averaging interval with the securities of his portfolio and assess the cu
How to allocate limited resources to projects that will yield the greatest long-term benefits is a problem that often arises in decision-making under uncertainty. For example, organizations may need to evaluate and select innovation projects with risky returns. Similarly, when allocating resources t
In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her terminal wealth exceeds a benchmark defined by her competitors’ p
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