Science AI Journal
Decision Sciences · Research topic

Open research questions in Risk and Portfolio Optimization

168 unresolved questions extracted from the limitations and future-work sections of 739 Risk and Portfolio Optimization papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • Extending the approach to Markov decision processes or stochastic games that involve angelic nondeterminism. Applying such extensions to solve a first-order extension of quantitative fixed-point logics with nondeterministic choice operations.

    A Hierarchy of Supermartingales for ω-Regular Verification · 2026 · DOI

  • Existing supermartingale-based certificates are not able to verify certain types of ω-regular properties. There is a need for more powerful certificates that can verify a wider range of properties. The paper identifies a gap in the existing approaches, which are not able to verify null recurrence.

    A Hierarchy of Supermartingales for ω-Regular Verification · 2026 · DOI

  • Investigating the application of the proposed framework to other problem domains - Exploring the use of different ambiguity sets in data-driven optimization - Developing more efficient algorithms for computing the resulting policies

    A Note on Piecewise Affine Decision Rules for Robust, Stochastic, and Data-Driven Optimization · 2026 · DOI

  • Formulation of a negative-dependence analogue of cMTP2 - Study of the potential stability under Markov products for the negative-dependence analogue of cMTP2

    An MTP2 property for conditional distributions · 2026 · DOI

  • The lack of a characterization of cMTP2 in terms of the Archimedean generator. The need for a basis for formulating and analyzing dependence properties for random vectors without imposing a particular partition on its components.

    An MTP2 property for conditional distributions · 2026 · 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 identifies a gap in the understanding of the effect of transaction costs on trading boundaries in the finite-horizon portfolio selection problem. 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

  • 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

  • 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 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 authors suggest that future research should focus on developing more efficient algorithms for solving S-shaped utility maximization problems. The authors suggest that future research should investigate the application of the proposed approach to more complex market models. The authors suggest that future research should compare the performances of different algorithms for solving S-shaped utility maximization problems.

    S-shaped Utility Maximization with VaR Constraint and Partial Information · 2026 · DOI

  • The paper identifies a gap in the literature on S-shaped utility maximization with unobservable drift coefficient. The authors note that prior work assumes observable drift coefficient, which may not be realistic in practice. The paper aims to contribute a novel approach to solving this problem.

    S-shaped Utility Maximization with VaR Constraint and Partial Information · 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 identifies a gap in the existing literature on DRPM problems under phi-divergence ambiguity. 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

  • To investigate the properties of M(alfa) in more detail. To apply the inequality to other functions and applications. To develop a general proof of monotonicity.

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

  • The classical form of Jensens inequality does not include memory effects. There is a need for a fractional-order generalisation of Jensens inequality involving memory effects. The existing literature does not provide a strict inequality that accounts for memory effects.

    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

  • 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

  • Modern portfolio theory struggles with extreme sensitivity to input parameters. The classic mean-variance model has a tendency to select highly concentrated portfolios.

    A multi-period robust portfolio optimization framework using yager’s entropy · 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

  • The limitations of common practices in portfolio optimization. The need for an alternative portfolio objective that can balance profit maximization and risk reduction.

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

  • There is a dearth of scholarly literature on remedies to the problem of Social Security insolvency, - Prior work has not fully addressed the optimal investment policy for national insurance funds

    The optimal asset allocation of national insurance funds · 2026 · DOI

Most-cited papers in Risk and Portfolio Optimization

Most recent work

Find a gap in your own Risk and Portfolio Optimization sub-topic

This page shows what the Risk and Portfolio Optimization literature already flags as unresolved. To narrow it to your specific question, run the guided finder — it searches the gap library on demand and checks candidates against 250M+ OpenAlex works.

Open the Research Gap Finder →

Related topics in Decision Sciences

Psychometric Methodologies and Testing
1,430 open questions
scientometrics and bibliometrics research
1,033 open questions
Evaluation and Performance Assessment
730 open questions
Technology Adoption and User Behaviour
537 open questions
Decision-Making and Behavioral Economics
484 open questions
Ethics in Business and Education
403 open questions
Meta-analysis and systematic reviews
313 open questions
Construction Project Management and Performance
301 open questions
168 open questions have been extracted from the limitations and future-work passages of 739 Risk and Portfolio Optimization papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

Tools for your next paper

Gaps & Literature SearchFind open questions in any field — 120,000+ open gaps mined from our own library.Pre-CheckIs your paper ready? A Tier 1–5 acceptance probability in seconds.Journal FinderA ranked shortlist of target journals from a 17,500-venue index.Duplicate Publication CheckerCheck prior-publication & salami-slicing risk across 8 sources.Citation GeneratorFreeA DOI or title → APA, MLA, Vancouver, Chicago, BibTeX, RIS. No signup.Graphical Abstract MakerFreeTurn your findings into a colorblind-safe graphical abstract.

Compare the category — Honest roundups of the AI research tools, ours listed alongside the alternatives.

Command palette

Jump anywhere, run any action.