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Open research questions in Stochastic processes and financial applications

275 gap statements mined from Stochastic processes and financial applications papers in our 7.9M-paper local library, which holds 2,415 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

  • Lack of effective methods for solving singular stochastic control problems with performance criteria dependent on the running infimum or supremum. Inadequacy of standard techniques in addressing the complexity introduced by this dependency.

    On the Singular Control of a Diffusion and Its Running Infimum or Supremum · 2026 · DOI

  • The paper does not provide a comprehensive comparison with other existing methods. The numerical results are limited to a specific example. The paper does not discuss the potential applications of the proposed algorithm in other fields.

    Stochastic Proximal Linearized ADMM for Sparse Distribution Control Problem Constrained by Random Elliptic Equation · 2026 · DOI

  • Future research can focus on extending the proposed algorithm to other nonsmooth stochastic optimization problems in Hilbert space. Future research can focus on developing more efficient algorithms for solving the sparse distributed control problem constrained by a random elliptic equation. Future research can focus on applying the proposed algorithm to other fields.

    Stochastic Proximal Linearized ADMM for Sparse Distribution Control Problem Constrained by Random Elliptic Equation · 2026 · DOI

  • The majority of stochastic differential delay equations cannot be solved explicitly. There is a gap in the understanding of the distribution function and properties of stochastic differential delay equations.

    Tail Distribution, Smoothness and Gaussian Density Estimates of Stochastic Differential Delay Equations · 2026 · DOI

  • Future research could focus on generalizing the results of the paper to higher dimensions. Future research could focus on developing a general theory for regularizing mean field games by noise.

    Intrinsic Regularization by Noise for 1d Mean Field Games · 2026 · DOI

  • There is a need to regularize mean field games by noise. There is a lack of examples of uniqueness forcing for generic mean field games set over an infinite dimensional set of probability measures.

    Intrinsic Regularization by Noise for 1d Mean Field Games · 2026 · DOI

  • Future research could explore the applications of skew-Normal diffusion processes. Future research could also explore the relationship between skew-Normal diffusion processes and other non-Gaussian processes.

    Skew-Normal Diffusions · 2026 · DOI

  • The valuation of swing options is a complex problem that involves solving PIDEs. There is a need for efficient numerical schemes for valuing swing options. The existing literature does not provide a comprehensive analysis of the numerical schemes for valuing swing options.

    Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps · 2026 · DOI

  • The lack of sufficient conditions for the convergence of approximating processes for Gaussian processes. The need for a methodology to construct approximating processes for Gaussian processes using renewal processes.

    Weak approximation for Gaussian processes from renewal processes · 2026 · DOI

  • The paper assumes the initial value is in L2(). It does not discuss the case where the drift grows faster than |z| log |z|. The results are limited to probabilistically strong solutions.

    L2-Solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise · 2026 · DOI

  • Future research should investigate the case where the drift grows faster than |z| log |z|. The development of new numerical methods is an area for future research. The application of the paper's approach to other equations with superlinear drifts is a potential direction.

    L2-Solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise · 2026 · DOI

  • The need to establish the uniform tightness of the set of all invariant measures.

    Invariant measures and their limiting behaviour of the Landau-Lifshitz-Bloch equation in unbounded domains · 2026 · DOI

  • The lack of understanding of the limiting behaviour of invariant measures. The need to extend the existence and uniqueness of solutions to unbounded domains.

    Invariant measures and their limiting behaviour of the Landau-Lifshitz-Bloch equation in unbounded domains · 2026 · DOI

  • In particular: Whether the DTE-mismatch construction produces a stable, observable proxy for across different market regimes has not been tested on real data.

    Engineering the Mean-Reversion Delay in Dispersion Trading: A Market-Implied Finite-Dimensional Proxy for High-Dimensional Correlation Manifolds · 2026 · DOI

  • Extensive numerical experiments assess the model accuracy by considering some stylized policies, but the model application is not limited to them being it able to manage different contract specifications.

    Fair valuations of insurance policies under multiple risk factors: A flexible lattice approach · 2024 · DOI

  • The paper does not discuss how the calibration problem in local stochastic volatility models is actually solved using the developed theory of nonregular McKean-Vlasov equations.

    Nonregular McKean–Vlasov Equations and Calibration Problem in Local Stochastic Volatility Models · 2026 · DOI

  • The strong convergence rates of numerical approximations for parabolic stochastic partial differential equations have yet to be studied thoroughly. The classical Lipschitz condition is not fulfilled in general for second-order parabolic semilinear SPDEs.

    OptimalStrongConvergenceRateofSpectralGalerkin Exponential Euler Scheme for Parabolic SPDEs · 2026 · DOI

  • The paper notes that the pricing of barrier options is more complex than that of European options.

    Semi-Analytical Pricing of Barrier Options in a Hybrid Model of Stochastic and Local Volatility · 2026 · DOI

  • To provide a comprehensive comparison of the numerical schemes.

    Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps · 2026 · DOI

  • The absence of the semimartingale property and the failure of the Markov property are noted as obstacles.

    Limit theorems for stochastic Volterra processes · 2026 · DOI

  • Further analysis of the properties of the novel integral operators - Application of the results to other stochastic control…

    On the Singular Control of a Diffusion and Its Running Infimum or Supremum · 2026 · DOI

  • The paper identifies a gap in the literature on the existence of a calibrated local stochastic volatility model. The paper identifies a gap in the literature on the approximation of McKean-Vlasov equations with nonregular coefficients.

    Nonregular McKean–Vlasov Equations and Calibration Problem in Local Stochastic Volatility Models · 2026 · DOI

  • To extend the results to other types of stochastic partial differential equations. To improve the accuracy of numerical simulations using the optimal strong convergence rates. To apply the scheme to problems in physics, engineering, and finance.

    OptimalStrongConvergenceRateofSpectralGalerkin Exponential Euler Scheme for Parabolic SPDEs · 2026 · DOI

  • The paper identifies a gap in the literature on non-Gaussian processes. The paper aims to fill this gap by introducing skew-Normal diffusion processes.

    Skew-Normal Diffusions · 2026 · DOI

  • The paper identifies a gap in the understanding of the connections between the Föllmer process and the DDPM. The paper identifies a gap in the analysis of sampling errors of the DDPM. The paper identifies a gap in the development of natural hyper-parameter settings of the DDPM sampler.

    A note on connections between the Föllmer process and the denoising diffusion probabilistic model · 2026

Most-cited papers in Stochastic processes and financial applications

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Open questions raised by papers listed on this page include: (1) Lack of effective methods for solving singular stochastic control problems with performance criteria dependent on the running infimum or supremum (“On the Singular Control of a Diffusion and Its Running Infimum or Supremum”, 2026); (2) Future research can focus on extending the proposed algorithm to other nonsmooth stochastic optimization problems in Hilbert space (“Stochastic Proximal Linearized ADMM for Sparse Distribution Control Problem…”, 2026); (3) Future research could focus on generalizing the results of the paper to higher dimensions (“Intrinsic Regularization by Noise for 1d Mean Field Games”, 2026); (4) Future research could explore the applications of skew-Normal diffusion processes (“Skew-Normal Diffusions”, 2026); (5) There is a need for efficient numerical schemes for valuing swing options (“Numerical methods for solving PIDEs arising in swing option pricing under a…”, 2026). 275 gap statements have been mined from Stochastic processes and financial applications papers in our 7.9M-paper local library, which holds 2,415 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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