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Open research questions in Risk and Portfolio Optimization

183 gap statements mined from Risk and Portfolio Optimization papers in our 7.9M-paper local library, which holds 1,451 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.

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What the literature leaves open

  • The need for robust theories and optimization methods for portfolio management. The complexity of investment decisions in a rapidly changing environment. The lack of effective methods for determining the most appropriate portfolio according to the investor's risk and return expectations.

    Artificial Bee Colony Algorithm for Portfolio Optimization: Comparative Performance Analysis on Two different Indices · 2026 · DOI

  • These results suggest that EVT can provide a practical alternative for training neural policies when the observations relevant to extreme risk are scarce.

    Deep catastrophic-risk-aware reinforcement learning · 2026

  • We investigate a data-driven quasi-concave maximization problem where information about the objective function is limited to a finite sample of data points.

    Robust Data-Driven Quasi-Concave Optimization · 2026 · DOI

  • This problem class is useful in a wide range of applications; however, its assimilation is partly limited by the lack of efficient solution schemes.

    Exact and Approximate Schemes for Robust Optimization Problems with Decision-Dependent Information Discovery · 2024 · DOI

  • Future research can explore the application of the results to other portfolio selection problems. The analysis can be extended to more complex models with multiple assets and risk factors.

    Comparative statics of trading boundary in finite-horizon portfolio selection problem with proportional transaction costs · 2026 · DOI

  • The paper does not provide a comprehensive comparison with other optimization techniques. The numerical experiments are limited to a few portfolio use cases. The paper suggests that future research should investigate asymptotic error properties.

    Mirror Descent Algorithms for Risk Budgeting Portfolios · 2026 · DOI

  • The gap is that prior work has focused on single-asset settings or neglected cross-impact effects. The gap is that prior work has not fully addressed the challenges of stochastic cross-effects in multi-asset trade execution.

    Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva–Wang-type framework · 2026 · DOI

  • The proofs rely on the assumption that γ^{-1/2} and related processes have almost-surely continuous paths, but discontinuities arising from market dislocations, liquidity crises, or regime breaks could violate this regularity condition. Robustness of the optimal execution strategy to jumps or discontinuities in market impact and correlation matrices remains unexplored.

    Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva–Wang-type framework · 2026 · DOI

  • Future research can extend the results to more general models with multiple jumps. The approach can be applied to other stochastic control problems with random time events. Numerical analysis of the results can be conducted to validate the findings.

    Stochastic Maximum Principle with Default · 2026 · DOI

  • The existing literature on stochastic control problems with default risk has several limitations. The stochastic maximum principle has not been established for controlled diffusion processes with a single jump at the default time. There is a need for a deeper understanding of optimal decision making in the presence of random time events.

    Stochastic Maximum Principle with Default · 2026 · DOI

  • The paper suggests that future research should focus on applying the proposed method to other problem domains. The paper suggests that future research should investigate the computational complexity of the proposed method. The paper suggests that future research should explore the applicability of the method to other types of ambiguity sets.

    Convexification of Fractional Distributionally Robust Probability Maximization Problems under Phi-Divergence Ambiguity · 2026 · DOI

  • The paper notes that existing methods do not provide a comprehensive reformulation method for DRPM problems. The paper identifies the need for a method that can be applied to various phi-divergences.

    Convexification of Fractional Distributionally Robust Probability Maximization Problems under Phi-Divergence Ambiguity · 2026 · DOI

  • The overriding limitation of this study is that the fractional refinement is based on the convexity of the exponential integral function on the support of the underlying random variable, which restricts the possible distributions to those with support on an interval where the exponential integral function is convex.

    Fractional form of Jensens Inequality for the Exponential Integral Function with Applications to Modeling Utility · 2026 · DOI

  • The gap is the lack of understanding of risk sharing among risk-seeking agents. The gap is the lack of explicit solutions for unconstrained and counter-monotonic inf-convolutions.

    Counter-monotonic risk sharing with heterogeneous distortion risk measures · 2026 · DOI

  • The paper suggests that future research could explore the application of the affine GARCH model to other areas of finance. The paper suggests that future research could investigate the use of other models for stochastic volatility. The paper suggests that future research could examine the impact of stochastic volatility on other types of investment decisions.

    Behavioral portfolio decisions in a GARCH world · 2026 · DOI

  • The paper notes that prior work has not considered the impact of stochastic volatility on behavioral portfolio decisions.

    Behavioral portfolio decisions in a GARCH world · 2026 · DOI

  • Future work will explore how the presence of ”loss-averse” agents affects market volatility and equilibrium prices compared to fully rational agents. This is particularly relevant for mechanistic interpretability and safety analysis, where identifying ”risk-aware” components in complex architectures is an open challenge.

    Perturbed Utility Functionals: A Functional-Analytic Framework for Adaptive Decision-Making · 2026 · DOI

  • The paper does not provide a complete characterization of uncertainty functionals that satisfy Jensen's inequality. The analysis is limited to general measurable spaces, and the results may not apply to specific cases.

    Uncertainty functionals revisited: Concavity and Jensen's inequality · 2026

  • To further clarify the theory of uncertainty functionals, it is important to understand whether all uncertainty functionals arise as the generalized entropy function of some proper scoring rule. Another important direction for future research is to refine the analysis of uncertainty functionals in the context of global sensitivity analysis.

    Uncertainty functionals revisited: Concavity and Jensen's inequality · 2026

  • Future research can focus on extending the approach to other parameterizations. Future research can also focus on comparing the approach with other methods. Future research can explore the application of the approach to various fields.

    Convex Bound of Nonlinear Dynamical Errors for Covariance Steering · 2026 · DOI

  • The existing literature does not provide a comprehensive analysis of the monotonicity of trading boundaries with respect to transaction cost rates.

    Comparative statics of trading boundary in finite-horizon portfolio selection problem with proportional transaction costs · 2026 · DOI

  • Investigating asymptotic error properties by establishing a central limit theorem for the stochastic MD algorithm. Comparing the proposed algorithms with other optimization techniques. Applying the algorithms to more portfolio use cases.

    Mirror Descent Algorithms for Risk Budgeting Portfolios · 2026 · DOI

  • The paper does not address formulations with nonlinearities, richer interdependencies, or dynamic constraints. The approach relies on a structured pricing oracle, which may not be applicable to all problem variants.

    Solving large-scale capital budgeting problems with column generation and optimization-based sorting · 2026 · DOI

  • To improve the accuracy of the model by incorporating more detailed data. To apply the model to other energy systems. To develop more advanced methods to solve the mixed-integer variables problem.

    Joint chance-constrained SDDP for Hydro-thermal Systems · 2026 · DOI

  • Further research on the application of the proposed objective to different types of investors. Investigation of the performance of the proposed objective in different market conditions.

    An alternative strategy for balancing profit maximization and risk reduction · 2026 · DOI

Most-cited papers in Risk and Portfolio Optimization

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Open questions raised by papers listed on this page include: (1) The lack of effective methods for determining the most appropriate portfolio according to the investor's risk and return expectations (“Artificial Bee Colony Algorithm for Portfolio Optimization: Comparative…”, 2026); (2) Future research can explore the application of the results to other portfolio selection problems (“Comparative statics of trading boundary in finite-horizon portfolio selection…”, 2026); (3) The paper suggests that future research should investigate asymptotic error properties (“Mirror Descent Algorithms for Risk Budgeting Portfolios”, 2026); (4) Robustness of the optimal execution strategy to jumps or discontinuities in market impact and correlation matrices remains unexplored (“Multi-asset optimal trade execution with stochastic cross-effects: An…”, 2026); (5) Future research can extend the results to more general models with multiple jumps (“Stochastic Maximum Principle with Default”, 2026). 183 gap statements have been mined from Risk and Portfolio Optimization papers in our 7.9M-paper local library, which holds 1,451 papers on the topic; the gaps come from whichever of those papers state one. They are mostly the research gaps the authors state and the papers' abstracts, plus future-work, limitations and challenges passages. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one, so you can read the original claim in context.

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