Publications

Selected Referred Publications: 

1. 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]

2. 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)

3. 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]

4. 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]  

5. 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)

6. 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)

7. 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)

8. 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)

9. 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)

10. 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)

11. 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)

Publications by Areas: 

Data-driven financial modeling and decision making:

1. 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)

2. 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]

Continuous-time Markov Chain Approximation and Applications:

1. 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]

2. 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]

3. 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]

4. 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]

5. 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]

6. 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)

7. 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]

8. 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)

9. 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)

10. 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)

11. 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)

12. 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)

13. 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)

14. Z.Cui, J.Kirkby, D.Nguyen. Full-fledged SABR through Markov Chains, Wilmott Magazine, 2019. forthcoming.  [Journal Link] [SSRN] [ResearchGate]  [GitHub Matlab Code]

15. 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)

Financial Econometrics and GARCH Option Pricing:

1. 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)

2. 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)

3. 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)

4. 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)

5. 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]

Stochastic Volatility and Volatility Derivatives: 

1. 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]

2. 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]

3. 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)

4. 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)

5. 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]

6. 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)

7. 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]

8. 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)

9. 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)

10. C. Bernard, Z. Cui, "Pricing Timer Options", Journal of Computational Finance, 2011, 15(1), 69-104. Available at:  [Journal Link] [talk1] [talk2]. [SSRN] (ABS1)

Non-convex Isotonic regression:

1. 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]

Monte Carlo Simulation and Sensitivity Analysis:

2. 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]

3. 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)

4. 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)

5. 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]

6. 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)

Applied Probability and Stochastic Drawdowns:

1. 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] 

2. 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]

3. 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]

4. 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)

5. 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]

6. 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)

Variable Annuity Modeling in Insurance Analytics:

1. 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)

2. 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]

3. 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)

4. 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)

Options Pricing and Hedging:

1. 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]

2. 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]

3. 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)

4. 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]

5. 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] 

6. 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]

7. 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]

8. 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]

9. 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)

10. 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]

Economic Theory:

1. 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)

2. Z. Cui, J. Deng, S. Lenkey.  Revisiting Advance Disclosure of Insider Trading, Economics Letters, 2019, 182, 78-81.  [Journal Link]  [ResearchGate] (ABS3)

3. Z. Cui, C. Wu, L. Zhu.  Explicit solution to the economic index of riskiness, Economics Letters, 2023, forthcoming.  [Journal Link]  [ResearchGate] (ABS3)

Systemic Risk

1. 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)

Foreign exchange market modeling

1. 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)

2. 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)

Quantile regression

1. 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)

Referred Book Chapter:

1. 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] 

Working Papers:

1. 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]

2. Z. Zhang, Z. Cui, "Laguerre series expansion for scale functions and its applications in risk theory", 2020.  Available at:  [ResearchGate]

3. 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]

4. 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]

5. 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]

6. Z. Cui, L. Zhu, "Exact Optimal Pricing Under the Multinomial Logit Choice Model with Network Effects," 2020, submitted. Available at: [SSRN] [ResearchGate]

7. Z.Cui, C. Lee, Y. Liu and K. Wang, "Failure and Rescue in Central Clearing Counterparty Design," 2019, working paper. Available at: [SSRN] [ResearchGate]

8. H. Cao, Z. Cui, Y. Liu.  "Discrete-time Variance-optimal Deep Hedging in Affine GARCH Models", 2020, working paper. Available at: [ResearchGate]

Permanent Working Papers:

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]

Media Coverage:

Z. Cui, "Bank of Montreal Capital Market Advanced Scholarship". 2011   [website]

Stevens Institute of Technology University News [website]

深圳晶报：  [website]

Awards and Recognitions:

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]