portfolio optimization

This paper addresses the problem of designing time-consistent optimal investment strategies under an explicit deviation-based conditional value-at-risk (DCVaR) constraint in continuous-time portfolio optimization—specifically, controlling the difference between terminal wealth’s CVaR and its expectation. To overcome the time-inconsistency inherent in conventional mean-CVaR frameworks, the paper introduces a novel methodology: within a complete market setting, it employs martingale methods to rigorously formulate and preserve the explicit DCVaR constraint, integrating convex optimization with stochastic analysis. The resulting optimal terminal wealth distribution is analytically tractable. The main contribution lies in establishing a dynamically consistent strategy with clear economic interpretation—namely, a state-dependent two-fund separation structure—that enhances both operational feasibility and robustness of risk-constrained asset allocation.

Traditional portfolio optimization methods face scalability limitations and insufficient modeling flexibility when handling multi-objective formulations, complex regulatory constraints (e.g., UCITS), tracking-error bounds, and large-scale datasets. To address these challenges, we propose an end-to-end multi-objective optimization framework grounded in gradient descent and automatic differentiation. The framework supports arbitrary risk–return objectives—such as CVaR and Sharpe ratio—in flexible combinations, and unifies hard and soft constraints within a single differentiable computational graph. It enables seamless transitions between single- and multi-objective settings without architectural modification. Empirically evaluated across six realistic scenarios, our approach matches or exceeds the performance of state-of-the-art solvers—including CVXPY and SKFOLIO—while substantially improving modeling expressiveness, computational scalability, and practical deployability. This work establishes a new paradigm for modern asset allocation that bridges theoretical rigor with engineering feasibility.

This paper addresses the optimal asset allocation problem for (re)insurers subject to regulatory Conditional Value-at-Risk (CVaR) constraints. To overcome the computational intractability of exact CVaR-constrained optimization, we propose a sample-average approximation (SAA)-based stochastic optimization framework. First, we establish the strong consistency of the SAA estimator under minimal distributional assumptions, derive an explicit convergence rate, and provide sufficient conditions for uniqueness of the optimal solution. The framework thus bridges theoretical rigor with computational tractability, yielding a provably convergent and implementable risk-compliant investment strategy. It enhances capital efficiency and portfolio robustness while ensuring regulatory compliance and prudent risk management.

To address the opacity of models, limited observation budgets, and uncontrolled risk in black-box portfolio management for finance, this paper proposes a risk-aware Bayesian optimization framework. Unlike conventional approaches that solely maximize expected return, we introduce an adaptive weighted Lagrangian estimator that jointly optimizes expected return maximization and observation variance minimization within a Gaussian process surrogate modeling framework. Crucially, we are the first to embed a variance constraint directly into the Lagrangian dual formulation and construct a variance-aware acquisition function. Extensive evaluation across five backtesting scenarios and three classes of black-box stock portfolio models demonstrates significant superiority over baseline methods. Ablation studies confirm the framework’s dual efficacy in mitigating risk accumulation and enhancing robust return performance.

This study addresses the optimal joint allocation of put options and trend-following strategies for tail risk management under multifaceted adverse scenarios—including market crashes, volatility repricing, and prolonged drawdowns. The authors develop a continuous-time Conditional Value-at-Risk (CVaR) framework that unifies both mechanisms within a single optimization objective. By modeling wealth, spot price, stochastic variance, and an exponentially weighted log-return signal as Markovian state variables, they derive the viscosity solution to the associated Hamilton–Jacobi–Bellman equation. A key innovation is the temporal decoupling of protective mechanisms: put options deliver immediate convexity-based protection, while trend following enhances resilience during sustained drawdowns. The framework further incorporates a four-dimensional diagnostic layer assessing conditional convexity, tail-event reliability, holding costs, and drawdown persistence. Monte Carlo simulations demonstrate that the hybrid strategy substantially reduces terminal CVaR, with optimal allocations highly sensitive to parameter calibration.

This study investigates the efficient optimization and tail risk measurement of heterogeneous actively managed ETF portfolios. Leveraging daily data from 30 actively managed ETFs and one fixed-income mutual fund, it systematically evaluates static and dynamic strategies—including mean-variance optimization, CVaR minimization, tangency portfolios, and extreme value theory approaches (Hill estimator and Peaks-Over-Threshold with Generalized Pareto Distribution)—under varying constraints that incorporate dependence structures, dynamic allocation, transaction costs, and multidimensional tail risk metrics. The findings indicate that the tangency portfolio delivers superior cumulative returns and risk-adjusted performance, while a dynamic long-only CVaR-95 strategy proves robustly effective. Despite aggregation, portfolios exhibit pronounced downside tail risk. Innovatively treating actively managed ETFs as a joint opportunity set, this work elucidates how strategy heterogeneity collectively shapes overall portfolio performance.

This study addresses portfolio optimization for commodity ETFs, accounting for their heavy-tailed return distributions. It proposes a dynamic, low-turnover Conditional Value-at-Risk (CVaR) optimization strategy that integrates extreme risk control with transaction cost constraints. Using daily data from 30 U.S. commodity ETFs, the authors employ ARMA–GARCH marginal models coupled with a Student-t copula to generate predictive scenarios, and compare mean-variance and CVaR approaches under both static rolling and dynamic frameworks. Empirical results show that minimum-risk and CVaR-based portfolios significantly improve Sharpe, Calmar, and STARR ratios. The proposed dynamic low-turnover CVaR strategy demonstrates robustness and practicality even after incorporating transaction costs, though additional mechanisms are required to manage extreme downside risk effectively.

This study addresses the optimization of optimized certainty equivalents (OCE), a risk measure widely employed in portfolio optimization and uncertainty quantification in machine learning. Focusing on unbounded random variables, it establishes the first OCE optimization framework by leveraging the duality between OCE and utility-based shortfall risk (UBSR). The work introduces a sample average approximation (SAA)-based OCE estimator and a corresponding stochastic gradient algorithm. Theoretical contributions include the design of an OCE gradient estimator, non-asymptotic mean squared error bounds, and convergence rates for the proposed algorithm. Empirical evaluations on portfolio optimization and uncertainty quantification tasks demonstrate the method’s effectiveness, offering both strong theoretical guarantees and practical performance.