X. Bi, Z. Cui, J. Fan, L. Yuan,, S. Zhang. "Optimal investment problem under behavioral setting: A Lagrange duality perspective", Journal of Economic Dynamics and Control, 2023, forthcoming. Available at: [SSRN] [ResearchGate]
K. Ding, Z. Cui. A general framework to simulate diffusions with discontinuous coefficients and local times. ACM Transactions on Modeling and Computer Simulation (TOMACS), 2022, 32(4). 1-29. (IF 2.33) Available at: [Journal Link] (LEAD ARTICLE)
Z.Cui, J. Kirkby, D.Nguyen, "Efficient simulation of generalized SABR and stochastic local volatility models", European Journal of Operational Research, 2021, 290(3), 1046-1062. (ABS4). Available at: [ResearchGate] [Slides] [Video Link]
J. Ma, W. Yang, and Z. Cui "CTMC integral equation method for American options under stochastic local volatility models", Journal of Economic Dynamics and Control, July 2021, 128, 104145. (ABS3) Available at: [Journal Link] [ResearchGate]
Z.Cui, M. Fu, J. Hu, Y. Liu, Y. Peng, L. Zhu. On the Variance of Single-Run Unbiased Stochastic Derivative Estimators, INFORMS Journal on Computing, 2020, 32(2), 390-407 [Journal Link] [ResearchGate] (UT Dallas 24 Journal List)
Z.Cui, J. Kirkby, D.Nguyen, "A unified data-driven framework for consistent financial valuation and risk measurement", European Journal of Operational Research, 2021, 289(1), 381-398. [Journal Link] (ABS4)
Z.Cui, J.Kirkby, D.Nguyen. Nonparametric density estimation by B-spline duality and applications, Econometric Theory, 2020, 36(2), 250-291. [Journal Link] [ResearchGate] [SSRN] (ABS4)
Z.Cui, J. Kirkby, D. Nguyen, "A general valuation framework for SABR and stochastic local volatility models", SIAM Journal on Financial Mathematics, 2018, 9(2), 520-563. Available at: [Journal Link] [Slides] (ABS2)
C. Bernard, Z. Cui, D.L. McLeish, "On the martingale property in stochastic volatility models based on time-homogeneous diffusions", Mathematical Finance, 2017, 27(1),194-223. Available at: [Online Appendix] [Journal Link] [Arxiv] [SSRN] (ABS3)
A. Badescu, Z. Cui and J-P. Ortega, "Non-Affine GARCH Option Pricing Models, Variance Dependent Kernels, and Diffusion Limits", Journal of Financial Econometrics 2017, 15(4), 602-648. Available at: [Journal Link] [SSRN] [ResearchGate] [Slides] (ABS3)
Z.Cui, J. Kirkby, D. Nguyen, A general framework for discretely sampled realized volatility derivatives in stochastic volatility models with jumps, European Journal of Operational Research, 2017, 262(1), 381-400. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS4)
Z.Cui, J. Kirkby, D.Nguyen, "A unified data-driven framework for consistent financial valuation and risk measurement", European Journal of Operational Research, 2021, 289(1), 381-398. [Journal Link] (ABS4)
Z,Cui, Z. Yu. A model-free Fourier cosine method for estimating the risk-neutral density. Journal of Derivatives, 2021, forthcoming. (ABS-2, IF 0.463) [Journal Link]
K. Ding, Z. Cui, X. Yang, Pricing arithmetic Asian and Amerasian options: a diffusion operator integral expansion approach. Journal of Futures Markets, 2022, forthcoming. Available at: [ResearchGate]
W. Zhong, Z. Cui, Z. Zhang. Efficient Valuation of Guaranteed Minimum Maturity Benefits in Regime Switching Jump Diffusion Models with Surrender Risk. Journal of Computational and Applied Mathematics, 2022, forthcoming . Available at: [Journal Link]
J. Ma, W. Yang, and Z. Cui "Convergence analysis for continuous-time Markov chain approximation of stochastic local volatility models: option pricing and Greeks", Journal of Computational and Applied Mathematics, 2022, 404, 113901. Available at: [Journal Link] [ResearchGate] [SSRN]
J. Ma, W. Yang, and Z. Cui "Analysis of Markov chain approximation for Asian options and occupation-time derivatives: Greeks and convergence rates", Mathematical Methods of Operations Research 2021, 93, 359-412. (ABS-1, IF 1.000). Available at: [SSRN] [ResearchGate]
Z.Cui, J. Kirkby, D.Nguyen, "Efficient simulation of generalized SABR and stochastic local volatility models", European Journal of Operational Research, 2021, 290(3), 1046-1062. (ABS4). Available at: [ResearchGate] [Slides] [Video Link]
K. Ding, Z. Cui, Y. Wang, "A Markov chain approximation scheme for option pricing under skew diffusions", Quantitative Finance, 2021, 21(3), 461-480. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS3)
Z.Cui, and S. Taylor "Pricing Discretely Monitored Barrier Options under Markov Processes using Markov Chain Approximations ", Journal of Derivatives (ABS2), 2021, Spring Issue. 28(3): 8-33. Available at: [SSRN] [ResearchGate]
Z.Cui, J.Kirkby, D.Nguyen, A general framework for time-changed Markov processes and applications, European Journal of Operational Research, 2019, 273 (2), 785-800. Available at: [Journal Link] [SSRN], [ResearchGate] (ABS4)
Z.Cui, J. Kirkby, D. Nguyen, "A general valuation framework for SABR and stochastic local volatility models", SIAM Journal on Financial Mathematics, 2018, 9(2), 520-563. Available at: [Journal Link] [Slides] (ABS2)
Z. Cui, C. Lee and Y. Liu, "Single-Transform Formulas for Pricing Asian Options in a General Approximation Framework under Markov Processes", European Journal of Operational Research, 2018, 266(3), 1134-1139. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS4)
Z.Cui, J. Kirkby, D. Nguyen, A general framework for discretely sampled realized volatility derivatives in stochastic volatility models with jumps, European Journal of Operational Research, 2017, 262(1), 381-400. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS4)
J.Kirkby, D.Nguyen, Z.Cui, "A unified approach to American and Barrier options under stochastic volatility models with jumps", Journal of Economic Dynamics and Control, 2017, 80, 75-100. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS3)
Z.Cui, J. Kirkby, D.Nguyen, "Equity-linked life insurance contracts with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps", Insurance: Mathematics and Economics, 2017, 74, 46-62. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS3)
Z.Cui, J.Kirkby, D.Nguyen. Full-fledged SABR through Markov Chains, Wilmott Magazine, 2019. forthcoming. [Journal Link] [SSRN] [ResearchGate] [GitHub Matlab Code]
R. Chatterjee, Z. Cui, J. Fan, M. Liu, "An efficient and stable method for short maturity Asian options", Journal of Futures Markets, 2018, 38(12), 1470-1486. Available at: [Journal Link] [SSRN] [ResearchGate] [Slides] (ABS 3)
Z.Cui, J.Kirkby, D.Nguyen. Nonparametric density estimation by B-spline duality and applications, Econometric Theory, 2020, 36(2), 250-291. [Journal Link] [ResearchGate] [SSRN] (ABS4)
A. Badescu, Z. Cui and J-P. Ortega, "Non-Affine GARCH Option Pricing Models, Variance Dependent Kernels, and Diffusion Limits", Journal of Financial Econometrics 2017, 15(4), 602-648. Available at: [Journal Link] [SSRN] [ResearchGate] [Slides] (ABS3)
A. Badescu, Y. Chen, M. Couch, and Z. Cui, "A Unified Valuation Framework for Variance Swaps Under Non-Affine Stochastic Volatility Models", Quantitative Finance, 2019, 19(2), 227-246. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS3)
A. Badescu, Z. Cui, and J-P Ortega, "Closed-form variance swap prices under general affine GARCH models and their continuous-time limits", Annals of Operations Research, 2019, 282, 27-57. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS 3)
H. Cao, A. Badescu, Z. Cui and S. Jarayaman, "Valuation of VIX and Target Volatility Options with Affine GARCH Models", 2020, Journal of Futures Markets, forthcoming. Available at: [ResearchGate]
Z.Zhao, Z.Cui, I.Florescu, "VIX Derivatives Valuation and Estimation Based on Closed-Form Series Expansions", International Journal of Financial Engineering, 2018, 5(2), 18 pages. Available at: [Journal link] [SSRN] [ResearchGate]
Z.Cui, D. Nguyen, H. Park, "An integral representation for elasticity and sensitivity for stochastic volatility models", Mathematics and Financial Economics, 2018, 12(2), 249-274. Available at: [Journal Link] [SSRN] [ResearchGate]
C. Bernard, Z. Cui, D.L. McLeish, "On the martingale property in stochastic volatility models based on time-homogeneous diffusions", Mathematical Finance, 2017, 27(1),194-223. Available at: [Online Appendix] [Journal Link] [Arxiv] [SSRN] (ABS3)
Z.Cui, J.L. Kirkby, G. Lian, D. Nguyen, "Integral Representation of Probability Density of Stochastic Volatility Models and Timer Options", International Journal of Theoretical and Applied Finance, 2017, 20(8), 1-32. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS2)
N. Yang, Y. Liu, Z. Cui, "Pricing Continuously Monitored Barrier Options under the SABR Model: A Closed-Form Approximation", Journal of Management Science and Engineering, 2017, 2(2), 116-131. Available at: [Journal Link] [SSRN] [ResearchGate]
A. Badescu, Z. Cui and J-P. Ortega, "A note on Wang transform for stochastic volatility pricing models", Finance Research Letters, 2016, 19, 189-196. Available at: [Journal Link], [SSRN] [ResearchGate] (ABS2)
C. Bernard, Z. Cui, D.L. McLeish, "Convergence of the discrete variance swap in time-homogeneous diffusion models", Quantitative Finance Letters, 2014, 2(1), 1-6. Available at: [Journal Link] [Arxiv] [SSRN]
C. Bernard, Z. Cui, "Prices and asymptotics for discrete variance swaps", Applied Mathematical Finance, 2014, 21(2), 140-173. Available at: [Journal Link] [SSRN] [Arxiv] (ABS2)
C. Bernard, Z. Cui, M. Forde, A. Jacquier, D.L. McLeish, A. Mijatovic, "Correction note for The large-maturity smile for the Heston model", Finance and Stochastics, 2013, 17(1), 223-224. Available at: [Journal Link] [SSRN] (ABS3)
C. Bernard, Z. Cui, "Pricing Timer Options", Journal of Computational Finance, 2011, 15(1), 69-104. Available at: [Journal Link] [talk1] [talk2]. [SSRN] (ABS1)
Z.Cui, C. Lee, L. Zhu and Y. Zhu, "Non-convex Isotonic Regression via the Myersonian Approach". Statistics and Probability Letters, 2021, 179, 109210. (ABS-2, IF 0.68) Available at: [Journal Link] [ResearchGate]
Z.Cui, C. Lee, L. Zhu and Y. Zhu, "On the optimal design of the randomized unbiased Monte Carlo estimators," Operations Research Letters, 2021, 49(4), 477-484. Available at: [Journal Link] [SSRN] [ResearchGate]
Z.Cui, M. Fu, J. Hu, Y. Liu, Y. Peng, L. Zhu. On the Variance of Single-Run Unbiased Stochastic Derivative Estimators, INFORMS Journal on Computing, 2020, 32(2), 390-407. [Journal Link] [ResearchGate] (UT Dallas 24 Journal List)
Z.Cui, M. Fu, Y. Peng and L. Zhu "Optimal Unbiased Estimation for Expected Cumulative Discounted Cost," European Journal of Operational Research, 2020, 2020, 286(2), 604-618. [Journal Link] [Arxiv] [SSRN] [ResearchGate] (ABS4)
G. Liu, Z. Cui, Y. Liu, J. Xie, "A simulation approach to financial options Greeks estimation under Levy processes", Journal of University of Science and Technology of China, 2017, 47(3), 262-266. Available at: [ResearchGate]
C. Bernard, Z. Cui, D.L. McLeish, "Nearly exact option price simulation using characteristic function", International Journal of Theoretical and Applied Finance, 2012, 15(7), 1-29. Available at: [Journal Link] [SSRN] [talk] (ABS2)
Z.Cui, D. Nguyen, "Magnitude and speed of consecutive market crashes in a diffusion model", Methodology and Computing in Applied Probability 2018, 20(1), 117-135. Available at: [Journal Link] [SSRN] [ResearchGate]
Z.Cui, D. Nguyen, "First hitting time of integral functional of diffusions and applications", Stochastic Models, 2017, 33(3), 376-391. Available at: [Journal Link] [SSRN] [ResearchGate]
Z.Cui, D. Nguyen, "Density of Verhulst process and Bessel process with constant drift", Lithuanian Mathematical Journal 2016, 56(4), 463-473. Available at: [Journal Link] [SSRN] [ResearchGate]
Z.Cui, D. Nguyen, "Omega diffusion risk model with surplus-dependent tax and capital injection", Insurance: Mathematics and Economics, 2016, 68, 150-161. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS3)
Z.Cui, J. Ma. "Stochastic areas of diffusions and application", Journal of Mathematical Analysis and Applications, 2016, 436(1), 79-93. Available at: [Journal Link] [ResearchGate]
Z. Cui, "A new proof of an Engelbert-Schmidt type zero-one law for time-homogeneous diffusions", Statistics and Probability Letters, 2014, 89, 118-123. Available at: [Journal Link] [Arxiv] [SSRN] (ABS2)
A. MacKay, M.C. Vachon, Z. Cui. "Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation", Quantitative Finance, 2023, 23(7), 1055-1078. Available at: [Journal Link] [Arxiv] [ResearchGate] (ABS3) (LEAD ARTICLE)
Z.Cui, J. Kim, G. Lian, and Y. Liu, "Risk measures for variable annuities: a Hermite series expansion approach," Journal of Management Science and Engineering, 2019, 4(2), 119-141. Available at: [Journal Link] [SSRN] [ResearchGate]
Z. Cui, R. Feng, A. MacKay, "Variable Annuities with VIX-linked Fee Structure under a Heston-type Stochastic Volatility Model", North American Actuarial Journal, 2017, 21(3), 458-483. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS2)
C. Bernard, Z. Cui and S. Vanduffel, "Impact of flexible periodic premiums on Variable Annuity guarantees", North American Actuarial Journal, 2017, 21(1), 63-86. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS2)
X. Yan, Y. Zhu, Z. Cui and S. Zhang, "Optimal Investment in Equity and VIX Derivatives", Journal of USTC, 2023, forthcoming. Available at: [SSRN] [ResearchGate]
J. Ma, Z. Cui, W. Li, "Laplace Bounds Approximation for American Options", Probability in the Engineering and Information Sciences, 2022, 36(2), 514-547. Available at: [SSRN] [ResearchGate]
G. Lian, SP. Zhu, R. Elliott, Z. Cui, "Semi-analytical valuation for discrete barrier options under time-dependent Levy processes", Journal of Banking and Finance, 2017, 75, 167-183. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS3)
Y. Xia, Z. Cui, "An Exact and Explicit Implied Volatility Inversion Formula", International Journal of Financial Engineering, 2018, 5(3), 29 pages. Available at: [Journal Link] [SSRN] [ResearchGate]
H. Cao, R. Chatterjee, and Z.Cui, "Options Valuation and Calibration for Leveraged Exchange-Traded Funds with Heston-Nandi and Inverse Gaussian GARCH Models", International Journal of Financial Engineering, 2019, forthcoming. Available at: [SSRN] [ResearchGate]
Z.Cui, J. Deng, "Shortfall risk through Fenchel duality", International Journal of Financial Engineering, 2018, 5(2), 14 pages. Available at: [Journal Link] [SSRN] [ResearchGate]
J. Ma, W. Li, Z. Cui, "Valuation of American strangles through an optimized lower-upper bound approach", Journal of Operations Research Society of China, 2018, 6(1), 25-47. Available at: [Journal Link] [SSRN] [ResearchGate]
J. Ma, Z. Zhou, Z. Cui, "Hybrid Laplace transform and finite difference methods for pricing American options under complex models", Computers and Mathematics with Applications, 2017, 74, 369-384. Available at: [Journal Link] [ResearchGate] [SSRN]
Y. Liu, Z. Cui, N. Zhang, "Integral Representation of Vega for American Put Options" , Finance Research Letters, 2016, 19, 204-208. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS2)
Z. Cui, D.L. McLeish, "Comment on 'Option pricing under the Merton model of the short rate' by Kung and Lee", Mathematics and Computers in Simulation, 2010, 81 (1), 1-4. Available at: [Journal Link] [SSRN]
Z. Cui, "Comment on 'Modelling non-monotone risk aversion using SAHARA utility functions'", Journal of Economic Theory, 2014, 153, 703-705. Available at: [Journal Link] [SSRN] (ABS4)
Z. Cui, J. Deng, S. Lenkey. Revisiting Advance Disclosure of Insider Trading, Economics Letters, 2019, 182, 78-81. [Journal Link] [ResearchGate] (ABS3)
Z. Cui, C. Wu, L. Zhu. Explicit solution to the economic index of riskiness, Economics Letters, 2023, forthcoming. [Journal Link] [ResearchGate] (ABS3)
Z.Cui, Q. Feng, R. Hu and B. Zou, "Systemic Risk and Optimal Fee Structure for Central Clearing Counterparty under Partial Netting", Operations Research Letters, 2018, 46(3), 306-311. Available at: [Journal Link] [SSRN] [ResearchGate] (ABS2)
Z.Cui, W. Qian, S. Taylor and L. Zhu "Detecting and Identifying Arbitrage in the Spot Foreign Exchange Market," Quantitative Finance, 2020, 20(1), 119-132. Available at: [Journal Link] [SSRN] [ResearchGate] [Conference Presentation] [Slides] (ABS3)
Z.Cui, and S. Taylor "Arbitrage Detection Using Max Plus Product Iteration on Foreign Exchange Rate Graphs," Finance Research Letters, 2020, 35, 101279. Available at: [Journal Link] [SSRN] [ResearchGate] [Conference Presentation] [Slides] (ABS2)
X. Wu, R. Liang, Z. Zhang, Z.Cui, "A unified fused Lasso approach for sparse and blocky feature selection in regression and classification" Computational Statistics and Data Analysis (CSDA), 2023, forthcoming. Available at: [Arxiv] (ABS3, IF 1.8)
Z.Cui, J.Kirkby, D.Nguyen. Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing, 2019, In: Yin G., Zhang Q. (eds) Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and its Applications, vol 164. Springer. Available at: [Springer Website] [SSRN] [ResearchGate]
J. Ma, W. Yang, Z.Cui. "Semimartingale and continuous-time Markov chain approximation for rough stochastic local volatility models", 2023 submitted. Available at: [ResearchGate] [SSRN] [Arxiv]
Z. Zhang, Z. Cui, "Laguerre series expansion for scale functions and its applications in risk theory", 2020. Available at: [ResearchGate]
Z.Cui, Z. Li, Y. Wu and M. Yu, "Variance risk premium and return predictability: Evidence from the Chinese SSE 50 ETF options," 2020. Available at: [ResearchGate] [SSRN]
Z. Zhang, Z. Cui, "A simple method for identifying the density function of the time to ruin by Laguerre series expansion", 2019, submitted. Available at: [ResearchGate]
Z.Cui, C. Lee, Y. Liu and L. Zhu, "Transform Analysis for Markov Processes and Applications: An Operator-based Approach," 2020, submitted. Available at: [SSRN] [ResearchGate]
Z. Cui, L. Zhu, "Exact Optimal Pricing Under the Multinomial Logit Choice Model with Network Effects," 2020, submitted. Available at: [SSRN] [ResearchGate]
Z.Cui, C. Lee, Y. Liu and K. Wang, "Failure and Rescue in Central Clearing Counterparty Design," 2019, working paper. Available at: [SSRN] [ResearchGate]
H. Cao, Z. Cui, Y. Liu. "Discrete-time Variance-optimal Deep Hedging in Affine GARCH Models", 2020, working paper. Available at: [ResearchGate]
C. Bernard, Z. Cui, D.L. McLeish, "Comment on the Large maturity smile for the Heston model", 2011, Available at SSRN: [pdf]
C. Bernard, Z. Cui, "A note on exchange options under stochastic interest rates ", 2010, Available at SSRN: [pdf]
Research Report:
Society of Actuaries Survey on Nested Stochastic Modeling, Society of Actuaries, 2015, Available at: [pdf]
Nested stochastic modeling for insurance companies. Society of Actuaries, 2016, Available at: [pdf]
Ph.D. Thesis:
Z. Cui, "Martingale Property and Pricing for Time-homogeneous Diffusion Models in Finance". 2013 Available at: [pdf]
Master Thesis:
Z. Cui, "Time change method in quantitative finance". 2010 Available at: [pdf]
Matlab Code: [link]
Z. Cui, "Bank of Montreal Capital Market Advanced Scholarship". 2011 [website]
Stevens Institute of Technology University News [website]
深圳晶报： [website]
Most cited article at SIAM Journal on Financial Mathematics [jpg]
Editor's Award for Excellence in Reviewing for European Journal of Operational Research [pdf]
Outstanding reviewer for European Journal of Operational Research [pdf]
Outstanding reviewer for Applied Mathematics and Computations [pdf]
Recognized reviewer for High Frequency [pdf]
Recognized reviewer for European Journal of Operational Research (37 papers) [pdf]
Recognized reviewer for Applied Mathematics and Computations (22 papers) [pdf]
Mathematical Olympiad Papers (In Simplified Chinese):
崔振嵛，张承宇, "一个几何不等式的简证"， 中等数学， 2004年第五期 Available at: [pdf]
崔振嵛，张承宇, "一个新代数不等式. 数学通讯， 2004年第22期 Available at: [pdf]