Portfolio Optimization

We investigate the static portfolio selection problem of S-shaped and non-concave utility maximization under first-order and second-order stochastic dominance (SD) constraints. In many S-shaped utility optimization problems, one should require a liquidation boundary to guarantee the existence of a f

We introduce a simple portfolio optimization strategy using ESG data with the Black-Litterman allocation framework. ESG scores are used as a bias for Stein shrinkage estimation of equilibrium risk premiums used in assigning Black-Litterman asset weights. Assets are modeled as multivariate affine nor

Probabilistic forecasting is crucial in multivariate financial time-series for constructing efficient portfolios that account for complex cross-sectional dependencies. In this paper, we propose Diffolio, a diffusion model designed for multivariate financial time-series forecasting and portfolio cons

Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical interactions among assets. Motivated by this observation, we

Robust asset allocation is a key challenge in quantitative finance, where deep-learning forecasters often fail due to objective mismatch and error amplification. We introduce the Signature-Informed Transformer (SIT), a novel framework that learns end-to-end allocation policies by directly optimizing

This study introduces a portfolio optimization framework to minimize mixed conditional value at risk (MCVaR), incorporating a chance constraint on expected returns and limiting the number of assets via cardinality constraints. A robust MCVaR model is presented, which presumes ellipsoidal support for

This paper investigates optimal investment and insurance strategies under a mean-variance criterion with path-dependent effects. We use a rough volatility model and a Hawkes process with a power kernel to capture the path dependence of the market. By adding auxiliary state variables, we degenerate a

A recent line of research has argued that causal factor models are necessary for portfolio optimization, claiming that structurally misspecified models inevitably produce inverted signals and nonviable frontiers. This paper challenges that view. We show, through theoretical analysis, simulation coun

Portfolio optimization has long been dominated by covariance-based strategies, such as the Markowitz Mean-Variance framework. However, these approaches often fail to ensure a balanced risk structure across assets, leading to concentration in a few securities. In this paper, we introduce novel risk m

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 whic

This paper develops a unified framework that integrates behavioral distortions into rational portfolio optimization by extracting implied probability weighting functions (PWFs) from optimal portfolios modeled under Gaussian and Normal-Inverse-Gaussian (NIG) return distributions. Using DJIA constitue

We investigate multi-period mean-risk portfolio optimization for long-horizon Defined Contribution plans, focusing on buffered Probability of Exceedance (bPoE), a more intuitive, dollar-based alternative to Conditional Value-at-Risk (CVaR). We formulate both pre-commitment and time-consistent Mean-b

We revisit the Bayesian Black-Litterman (BL) portfolio model and remove its reliance on subjective investor views. Classical BL requires an investor “view”: a forecast vector $q$ and its uncertainty matrix $Ω$ that describe how much a chosen portfolio should outperform the market. Our key idea is to

Portfolio optimization requires dynamic allocation of funds by balancing the risk and return tradeoff under dynamic market conditions. With the recent advancements in AI, Deep Reinforcement Learning (DRL) has gained prominence in providing adaptive and scalable strategies for portfolio optimization.

The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of t

Style investing creates asset classes (or the so-called “styles”) with low correlations, aligning well with the principle of “Holy Grail of investing” in terms of portfolio selection. The returns of styles naturally form a tensor-valued time series, which requires new tools for studying the dynamics

This study presents the Adaptive Minimum-Variance Portfolio (AMVP) framework and the Adaptive Minimum-Risk Rate (AMRR) metric, innovative tools designed to optimize portfolios dynamically in volatile and nonstationary financial markets. Unlike traditional minimum-variance approaches, the AMVP framew

We study the allocation of synthetic portfolios under hierarchical nested, one-factor, and diagonal structures of the population covariance matrix in a high-dimensional scenario. The noise reduction approaches for the sample realizations are based on random matrices, free probability, deterministic

A diversification quotient (DQ) quantifies diversification in stochastic portfolio models based on a family of risk measures. We study DQ based on expectiles, offering a useful alternative to conventional risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). The expectile-based DQ a

Portfolio optimization is a ubiquitous problem in financial mathematics that relies on accurate estimates of covariance matrices for asset returns. However, estimates of pairwise covariance could be better and calculating time-sensitive optimal portfolios is energy-intensive for digital computers. W