Jinniao QiuMATHEMATICS · UCALGARY

JINNIAO QIU · UNIVERSITY OF CALGARY

Research & Teaching

I work at the interface of stochastic analysis, control and game theory, and partial differential equations. A recurring question is how to characterize, compute, and use optimal decisions when a system depends on random information, its past evolution, or the distribution of interacting states. I develop probabilistic and numerical methods for PDEs and problems involving randomness and local/nonlocal interactions in Markovian/non-Markovian settings. Applications include optimization, games, operational research, mathematical finance and economics, and other scientific fields.

My teaching at the University of Calgary for the 2026–2027 academic year includes Introduction to Mathematical Finance (MATH 383), Differential Equations III (MATH 605), and Computational Finance (MATH 583 / 683). Enrolled students can find course materials and announcements through D2L.

Publications and preprints

Updated .

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PDEs, SPDEs, Stochastic control and mathematical finance

  1. C. Bayer, U. Horst, and J. Qiu, A functional limit theorem for limit order books with state dependent price dynamics, The Annals of Applied Probability, 27 (2017), pp. 2753–2806.
  2. C. Bayer, J. Qiu, and Y. Yao, Pricing options under rough volatility with backward SPDEs, SIAM Journal on Financial Mathematics, 13 (2022), pp. 179–212. [arXiv]
  3. E. Bayraktar, H. Cheung, I. Ekren, J. Qiu, H. M. Tai, and X. Zhang, Viscosity solutions of fully second-order HJB equations in the Wasserstein space, SIAM Journal on Control and Optimization, 64 (2026), pp. 2250–2280.
  4. E. Bayraktar and J. Qiu, Controlled reflected SDEs and Neumann problem for backward SPDEs, The Annals of Applied Probability, 29 (2019), pp. 2819–2848.
  5. H. Cheung, H. M. Tai, and J. Qiu, Viscosity solutions of a class of second order Hamilton–Jacobi–Bellman equations in the Wasserstein space, Applied Mathematics & Optimization, 91 (2025), p. 23.
  6. K. Du, J. Qiu, and S. Tang, LpL^p theory for super-parabolic backward stochastic partial differential equations in the whole space, Applied Mathematics & Optimization, 65 (2012), pp. 175–219.
  7. R. Elliott, J. Qiu, and W. Wei, Neumann problem for backward SPDEs with singular terminal conditions and application in constrained stochastic control under target zone, Stochastic Processes and their Applications, 148 (2022), pp. 68–97.
  8. G. Fu, U. Horst, and J. Qiu, Maximum principle for quasi-linear reflected backward SPDEs, Journal of Mathematical Analysis and Applications, 456 (2017), pp. 307–336.
  9. P. Graewe, U. Horst, and J. Qiu, A non-Markovian liquidation problem and backward SPDEs with singular terminal conditions, SIAM Journal on Control and Optimization, 53 (2015), pp. 690–711.
  10. U. Horst, J. Qiu, and Y. Yang, Optimal resource extraction under distribution learning and infinite-horizon stochastic Hamilton–Jacobi equations, arXiv preprint arXiv:2609.17717, (2026).
  11. U. Horst, J. Qiu, and Q. Zhang, A constrained control problem with degenerate coefficients and degenerate backward SPDEs with singular terminal condition, SIAM Journal on Control and Optimization, 54 (2016), pp. 946–963.
  12. J. Ma, M. Ogunsolu, J. Qiu, and A. D. Sezer, Credit risk pricing in a consumption-based equilibrium framework with incomplete accounting information, Mathematical Finance, 33 (2023), pp. 666–708.
  13. K. Mirzaei and J. Qiu, Strong measurability and adapted approximations with applications to non-Markovian control, arXiv preprint arXiv:2609.27478, (2026).
  14. J. Qiu, Weak solution for a class of fully nonlinear stochastic Hamilton–Jacobi–Bellman equations, Stochastic Processes and their Applications, 127 (2017), pp. 1926–1959.
  15. , Viscosity solutions of stochastic Hamilton–Jacobi–Bellman equations, SIAM Journal on Control and Optimization, 56 (2018), pp. 3708–3730. [arXiv]
  16. , Stochastic path-dependent Hamilton-Jacobi-Bellman equations and controlled stochastic differential equations with random path-dependent coefficients, arXiv preprint arXiv:2006.13043, (2020).
  17. , Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton–Jacobi equations, Stochastic Processes and their Applications, 154 (2022), pp. 1–25.
  18. J. Qiu and S. Tang, Maximum principle for quasi-linear backward stochastic partial differential equations, Journal of Functional Analysis, 262 (2012), pp. 2436–2480.
  19. J. Qiu, A. F. Ware, and Y. Yang, Stochastic path-dependent volatility models for price–storage dynamics in natural gas markets and discrete-time swing option pricing, Journal of Computational Finance, 29 (2026), pp. 69–109. [arXiv]
  20. J. Qiu and W. Wei, On the quasi-linear reflected backward stochastic partial differential equations, Journal of Functional Analysis, 267 (2014), pp. 3598–3656.
  21. , Uniqueness of viscosity solutions of stochastic Hamilton-Jacobi equations, Acta Mathematica Scientia, 39 (2019), pp. 857–873.
  22. J. Qiu and Y. Yang, Optimal control of infinite-dimensional differential systems with randomness and path-dependence and stochastic path-dependent Hamilton–Jacobi equations, ESAIM: Control, Optimisation and Calculus of Variations, 30 (2024), p. 12.

Probabilistic and stochastic approaches in PDEs

  1. H. Cheung, J. Qiu, and Y. Yang, Feynman-Kac formula for time-dependent nonlinear Schrödinger equations with applications in numerical approximations, Stochastic Processes and their Applications, 202 (2026), p. 105091.
  2. F. Delbaen, J. Qiu, and S. Tang, Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space, Stochastic Processes and their Applications, 125 (2015), pp. 2516–2561.
  3. R. C. Fetecau, H. Huang, and J. Qiu, Swarming models with specular boundary condition and environmental noise, arXiv preprint arXiv:2304.02130, (2023).
  4. H. Huang and J. Qiu, The microscopic derivation and well-posedness of the stochastic Keller–Segel equation, Journal of Nonlinear Science, 31 (2021), p. 6.
  5. J. Qiu, Hörmander-type theorem for Itô processes and related backward SPDEs, Bernoulli, 24 (2018), pp. 956–970.
  6. , L2L^2-theory of linear degenerate SPDEs and LpL^p (p>0p>0) estimates for the uniform norm of weak solutions, Stochastic Processes and their Applications, 130 (2020), pp. 1206–1225.
  7. J. Qiu and S. Tang, On backward doubly stochastic differential evolutionary system, arXiv preprint arXiv:1309.4152, (2013).
  8. J. Qiu, S. Tang, and Y. You, 2D backward stochastic Navier–Stokes equations with nonlinear forcing, Stochastic Processes and their Applications, 122 (2012), pp. 334–356.

Optimizations, games, and numerics

  1. G. Borghi, H. Huang, and J. Qiu, A particle consensus approach to solving nonconvex-nonconcave min-max problems, SIAM Journal on Control and Optimization, 64 (2026), pp. 1573–1601.
  2. P. Cardaliaguet, M. Grigorova, T. Mastrolia, J. Qiu, and J. Zhang, New trends and challenges in stochastic differential games, Workshop report 24w5277, Banff International Research Station, 2024.
  3. E. Chenchene, H. Huang, and J. Qiu, A consensus-based algorithm for non-convex multiplayer games, Journal of Optimization Theory and Applications, 206 (2025), p. 45.
  4. H. Cheung and J. Qiu, SCMO: Stochastic control for optimization over probability measures on infinite-dimensional spaces, arXiv preprint arXiv:2609.14548, (2026). [Code]
  5. C. Cipriani, H. Huang, and J. Qiu, Zero-inertia limit: from particle swarm optimization to consensus-based optimization, SIAM Journal on Mathematical Analysis, 54 (2022), pp. 3091–3121.
  6. S. Grassi, H. Huang, L. Pareschi, and J. Qiu, Mean-field particle swarm optimization, in Modeling and simulation for collective dynamics, vol. 40 of Lecture Notes Series, Institute for Mathematical Sciences, World Scientific, 2023, pp. 127–193.
  7. H. Huang and J. Qiu, On the mean-field limit for the consensus-based optimization, Mathematical Methods in the Applied Sciences, 45 (2022), pp. 7814–7831.
  8. H. Huang, J. Qiu, and K. Riedl, On the global convergence of particle swarm optimization methods, Applied Mathematics & Optimization, 88 (2023), p. 30. [arXiv]
  9. , Consensus-based optimization for saddle point problems, SIAM Journal on Control and Optimization, 62 (2024), pp. 1093–1121. [arXiv]
  10. H. U. Molla, M. Backhouse, A. Banarjee, and J. Qiu, A deep learning-based method for fully coupled non-Markovian FBSDEs with applications, arXiv preprint arXiv:2511.08735, (2025).
  11. H. U. Molla and J. Qiu, Numerical approximations of coupled forward–backward SPDEs, Stochastic Analysis and Applications, 41 (2023), pp. 291–326.
  12. , A policy iteration scheme for semilinear stochastic Hamilton-Jacobi-Bellman equations with exponential convergence, arXiv preprint arXiv:2607.29024, (2026).
  13. J. Qiu, Stochastic control methods for optimization, arXiv preprint arXiv:2601.01248, (2026).
  14. J. Qiu and J. Zhang, Stochastic differential games with random coefficients and stochastic Hamilton–Jacobi–Bellman–Isaacs equations, The Annals of Applied Probability, 33 (2023), pp. 889–930.