Reader in Financial Mathematics
Mail: Department of Mathematics,
Imperial College, London
SW7 2BZ, UK
Tel: +44(0) 20 7594 8539
Fax: +44(0) 20 7594 1191
Stochastic control and mathematical finance.
Selected refereed papers:
- J.T. Ma, W.Y. Li, H. Zheng, Dual Control Monte-Carlo Method for Tight Bounds of Value Function in Regime Switching Utility Maximization, European J Operational Research , to appear.
- J.W. Gu, M. Steffensen, H. Zheng, Optimal Dividend Strategies of Two Collaborating Businesses
in the Diffusion Approximation Model, Mathematics of Operations Research, to appear.
- K.C. Wong, S.C.P. Yam, H. Zheng, Utility-Deviation-Risk Portfolio Selection, SIAM J Control Optimization, to appear. (pdf)
- Y.T. Huang, Q.S. Song, H. Zheng (2017), Weak Convergence of Path-dependent SDEs in Basket CDS Pricing with Contagion Risk, SIAM J Financial Mathematics 8, 1-27. (pdf)
- J.W. Gu, B. Jiang, W.K. Ching, H. Zheng (2016), On Modeling Economic Default Time: A Reduced-Form Model Approach, Computational Economics 47, 157-177. (pdf)
- B. Bian, N. Wu, H. Zheng (2016), Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact, Discrete and Continuous Dynamical Systems (Series B) 21, 1401-1420. (pdf)
- J.T. Ma, D.Y. Deng and H. Zheng (2016), Convergence Analysis and Optimal Strike Choice for Static Hedges of General Path-independent Payoffs, Quantitative Finance 16, 593-603.
- C. Liu and H. Zheng (2016), Asymptotic Analysis for Target Asset Portfolio Allocation with Small Transaction Costs, Insurance: Mathematics and Economics 66, 59-68.
- N. Westray and H. Zheng (2015), Constrained Nonsmooth Utility Maximization on the Positive Real Line, Mathematical Control and Related Fields 5, 679-695.
- B. Bian, S. Hu, Q. Yuan, H. Zheng (2015), Constrained Viscosity Solution to the HJB Equation Arising in
Perpetual American Employee Stock Options Pricing, Discrete and Continuous Dynamical Systems (Series A) 35, 5413-5433. (pdf)
- X. Dong and H. Zheng (2015), Intensity Process for a Pure Jump Levy Structural Model with Incomplete Information, Stochastic Processes and Their Applications 125,
- Y. Li and H. Zheng (2015), Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models, Applied Mathematics and Optimization 71, 39-77. (arxiv)
- B. Bian and H. Zheng (2015), Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions, J Economic Dynamics and Control 51, 28-49.
- G. Xu and H. Zheng (2014), Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Models, International J Theoretical and Applied Finance 17, 1-15. (arxiv)
- J.W. Gu, W.K. Ching, T.K. Siu, H. Zheng (2014), On Reduced Form Intensity-based Model with Trigger Events,
J Operations Research Society 65, 331-339.
- J.W. Gu, W.K. Ching, T.K. Siu, H. Zheng (2013),
On Pricing Basket Credit Default Swaps,
Quantitative Finance 13, 1845-1854.
- J.W. Gu, W.K. Ching, T.K. Siu, H. Zheng (2013), On Modeling Credit Defaults: A Probabilistic Boolean Network Approach, Risk and Decision Analysis 4, 119-129. (pdf)
- H. Zheng (2013), Contagion Models a la carte: Which One to Choose?, Quantitative Finance 13, 399-405.
- B. Bian, S. Miao, H. Zheng (2011), Smooth Value Functions for a Class of Nonsmooth
Utility Maximization Problems,
SIAM J Financial Mathematics 2, 727-747.
- N. Westray and H. Zheng (2011), Minimal Sufficient Conditions for a Primal Optimizer in Nonsmooth
Utility Maximization, Finance and Stochastics 15, 501-512. (pdf)
- J. Lin, G. Liang, S. Wu, H. Zheng (2011), The Valuation of the Basket CDSs in the Primary-Subsidiary Model, Asia-Pacific J Operational Research 28, 213-238.
- C. Czichowsky, N. Westray, H. Zheng (2011), Convergence in the Semimartingale Topology and Constrained Portfolios,
Seminaire de Probabilites XLIII, 395-412.
- G. Xu and H. Zheng (2010), Basket Options Valuation for a Local Volatility Jump-Diffusion Model
with the Asymptotic Expansion Method,
Insurance: Mathematics and Economics 47, 415-422.
- G. Xu and H. Zheng (2009), Approximate Basket Options Valuation for a Jump-Diffusion Model,
Insurance: Mathematics and Economics 45, 188-194.
- H. Zheng (2009), Efficient Frontier of Utility and Conditional VaR, Mathematical
Methods of Operations Research 70, 129-148.
- L. Jiang and H. Zheng (2009), Basket CDS Pricing with Interacting Intensities,
Finance and Stochastics 13, 445-469.
- N. Westray and H. Zheng (2009), Constrained Nonsmooth Utility Maximization without Quadratic Inf-Convoluiton, Stochastic Processes
and Their Applications 119, 1561-1579.
- Y.K. Shen and H. Zheng (2008), Jump Liquidity Risk and its Impact on CVaR, J Risk Finance 9, 477-491.
- H. Zheng (2007), Macaulay Duration for Nonparallel Shifts, Annals of Operations Research 151, 179-191.
- H. Zheng (2006), Interaction of Credit and
Liquidity Risks, J Banking Finance 30, 391-407.
- H. Zheng (2006), Efficient Hybrid Methods for Portfolio Credit Derivatives,
Quantitative Finance 6, 349-357.
- R.B. Vinter and H. Zheng (2003),
Some Finance Problems Solved with Nonsmooth Optimization
Techniques, J Optimization, Theory and
Application 119, 1-18.
- D.E. Allen, L.C. Thomas, H. Zheng (2003),
The Duration Derby: A Comparison of Duration Strategies
in Asset Liability Management,
J Bond Trading Management 1, 371-380.
- M. R. Pinho, R. B. Vinter, H. Zheng (2001), A Maximum Principle for Optimal Control
Problems with Mixed Constraints,
IMA J Mathematical Control and Information 18, 189-205.
- D.E. Allen, L.C. Thomas, H. Zheng (2000),
Stripping Coupons with Linear Programming,
J Fixed Income 10, 80-87.
- R. B. Vinter and H. Zheng (2000), Necessary Conditions for Free End-Time, Measurably Time
Dependent Optimal Control
Problems with State Constraints, J Set-Valued
Analysis 8, 11-29.
- M.R. Pinho and H. Zheng (1999), Conjugate Points for Optimal Control
Problems with State-Dependent Control Constraints,
CRC Research Notes in Mathematics: Systems Modeling
and Optimization, Ed. MP Polis, Chapman and Hall, 162-170.
- R. B. Vinter and H. Zheng (1998), Necessary Conditions for Optimal Control Problems with State Constraints,
Trans. American Mathematical Society 350, 1181-1204.
- A. Gautier, F. Granot, H. Zheng (1998), Qualitative Sensitivity Analysis
in Monotropic Programming, Mathematics
of Operations Research 23, 695-707.
- R. B. Vinter and H. Zheng (1997), The Extended Euler Lagrange Condition
for Nonconvex Variational Problems,
SIAM J Control Optimization 35, 56-77.
- P. D. Loewen and H. Zheng (1995), Epi-Differentiability of Integral
Functionals with Applications,
Trans. American Mathematical Society
- P. D. Loewen and H. Zheng (1994), Generalized Conjugate Points for
Optimal Control Problems, J Nonlinear Analysis,
Theory, Method and Applications 22, 771-791.
- H. Zheng (1994), Second Order Necessary Conditions for Differential
Inclusion Problems, Applied Mathematics and Optimization
I was the principal organizer of the
Workshop on Stochastics, Control and Finance
at Imperial College on April, 12-14, 2010
(programme and abstracts). The proceedings of the workshop has been published in a special issue of Stochastics 84, Issue 5-6, 2012, see the foreword
- Statistical Distribution Theory (MSc in Mathematics and Finance).
Topics include basic concepts and results in probability
theory, common and advanced statistical distributions, statistical estimators
and sampling distributions, random variate generators, multivariate distribuitons,
sum of correlated random variables, copulas,
and other topics of current interest in statistics and mathematical finance.
- Mathematical Options Pricing (MSc in Mathematics and Finance).
This course introduces continuous time mathematical optiopns pricing theory. Topics include some advanced stochastic analysis, Black-Scholes options pricing and hedging (call, put, barrier, lookback etc.), multi-asset options pricing (Margrabe, currency, etc.), American options pricing.