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Open research questions in Stochastic processes and financial applications

209 unresolved questions extracted from the limitations and future-work sections of 712 Stochastic processes and financial applications papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • Esser and Loosveldt have recently resolved a long-standing open problem in the folklore by proving that fractional Brownian motion (fBm) has slow points in the sense of Kahane, following a rich theory of slow points developed for Brownian motion and other, related, self-similar Markov processes.

    On the slow points of fractional Brownian motion · 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

  • 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

  • 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 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 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 paper identifies challenges in addressing the no-ceiling case. The paper requires novel arguments to address these challenges. The paper needs to relax the constraints on the solution to define its solution as in Definition 4.1.

    Optimal Dividend Payout with Path-dependent Drawdown Constraint · 2026 · DOI

  • Future research could extend the results to more general models and settings. Future research could explore the application of the PDE-based framework to other problems in actuarial science and financial mathematics.

    Optimal Dividend Payout with Path-dependent Drawdown Constraint · 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

  • The complexity of the mixed fractional Heston model, which involves correlated fractional Brownian motions. The need for a rigorous convergence analysis of the proposed collocation method. The challenge of solving a system of nonlinear algebraic equations to obtain the unknown coefficients.

    A Collocation Method Using Diagonal Polynomials for Pricing Geometric Asian Options Under the Mixed Fractional Heston Model · 2026 · DOI

  • The lack of efficient numerical methods for pricing geometric Asian options under the mixed fractional Heston model. The need for a rigorous convergence analysis of the proposed collocation method.

    A Collocation Method Using Diagonal Polynomials for Pricing Geometric Asian Options Under the Mixed Fractional Heston Model · 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 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 existing literature on valuing barrier options in a hybrid model of stochastic volatility and constant elasticity of variance. 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 develop more efficient numerical schemes for valuing swing options. To apply the numerical schemes developed in this paper to other types of financial derivatives. 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 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 identifies the gap in studying stochastic Volterra equations with operator-valued Volterra kernels. 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

  • The paper assumes the initial value is in L2([0, 1]). 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

  • Extension of the PDE approach to more general short-rate models. Development of more efficient numerical methods. Application of the PDE approach to other financial derivatives.

    Short-rate models with stochastic discontinuities: A PDE approach · 2026 · DOI

  • The lack of a general short-rate model that incorporates discontinuities at fixed times with random sizes. The need for numerical methods for pricing interest rate derivatives with stochastic discontinuities.

    Short-rate models with stochastic discontinuities: A PDE approach · 2026 · DOI

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209 open questions have been extracted from the limitations and future-work passages of 712 Stochastic processes and financial applications papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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