Professor Dr.Zongxia Liang


Welcome to my homepage


简介:梁宗霞, 博士,教授,博士生导师。1996年获中国科学院应用数学所概率统计专业博士学位。1996年至1998年在北京大学数学院概率统计系做博士后研究工作。1998年开始
在清华大学数学科学系从事科研和教学工作。20029月至200311月作为客座研究员访问美国麻省理工学院(MIT)数学系。20089月至20098月韩国国立首尔大学(SNU)
客座教授。研究领域为概率论和随机分析,保险数学与精算科学, 金融数学与金融工程, 保险经济学与金融经济学,随机控制与优化等。在Mathematical Finance,  Insurance:Mathematics 
and Economics, North American Actuarial Journal, Stochastic Processes and Their Applications, Ann.Inst.Henri Poincaré(B) Probab.Stat., Journal of Functional Analysis等国际著名期刊杂志上
表论文近六十篇。在保险数学、金融数学与精算科学: 分红与注资, 比例再保险, DC养老金风险管理, 投资组合与随机控制, 和随机分析:局部时过程与随机微分方程等方向做出了系列
原创性工作。自2000年至今, 培养和指导博士后,博士研究生和硕士研究生及访问学者近四十余名(包括在读), 目前他们在中国科学院、中国人民大学、中国人民银行(总部)、中国保险
监督管理委员会、中国人寿保险公司(总部)、中国银行(总部)等科研机构、高校、国家行政部门和国家金融机构等部门工作, 国际金融机构及在美国政府部门、高校工作和攻读博
士学位等

联系方式与办公室

E-mail: liangzongxia@mail.tsinghua.edu.cn

Homepage: http://faculty.math.tsinghua.edu.cn/~zliang/

Office: 理科楼 A-121.

TeL.:+86-10-62796925

Office Hours: by appointment only.


 

教学、科研等方面


Research Fields


Probability Theory, Stochastic Analysis and Stochastic Controls

Stochastic differential quations; Local times; Stochastic flows; Stochastic control and optimization problems; Stochastic dynamic programming; Malliavin calculus.

Insurance Mathematics and Actuarial Science

Stochastic control and optimization Problems in insurance; Dividend; Portfolio theory; Ruin probability; Pricing theory; Risk theory; Risk management; Reinsurance; Utility theory;

Equilibrium theory; Life insurance; DC and DB pensions; Liabilities; Insurance Modeling; Risk measure; Robust control and optimization; Ambiguity and risk.

(1) Portfolio selection strategy: Optimal investment; Consumptions; Dividend; Reinsurance; Proportional reinsurance; Non-proportional reinsurance; Mean-variance utility; Dynamic asset allocation and optimal portfolio choice; Robust portfolio selection; Insurance product design.

(2) Pricing and hedging in insurance products: Mortality risk; Ambiguity and risk; Inflation-linked annuities; Stochastic interest rate; Stochastic volatility; Life insurance liabilities; Longevity bonds; Guarantee; Life and non-life insurance contracts; Longevity-linked security.

(3) Pensions systems: Optimal portfolio selection problem in defined contribution(DC) pension plans and defined benefit(DB) pension plans based on families of suitable utility functions; Health insurance.

(4) Risk theory, robust control and optimization problems: Robust control and optimization problems under ambiguity in Insurance; Risk models; Ruin probability; Risk measures; Risk-sharing arrangement and risk anagement; Credit default swaps; Robust optimization of credit portfolios.

Mathematical Finance and Financial Engineering

Robust control and optimization problems in Finance; Derivative pricing; Portfolio theory; Structured finance; Derivative securities; Credit risk; Financial modeling; Interest rates(stochastic model); Corporate finance; Risk management; Dynamic stochastic general equilibrium theory; Heterogeneous agent models; Utility theory; Market structure and market models; Stochastic nonconvex and nonlinear programming; Stochastic minimax problems.

(1) Optimal investment: Portfolio selection with tax/transaction costs,…, trading strategies; Stochastic model; Structured finance; Dynamic stochastic general equilibrium theory; Game Theory; Resource and cost allocation; Utility theory; Stochastic nonconvex and nonlinear control optimization problems with heterogeneous agent models; Robust consumption-investment problems with ambiguity; Stochastic minimax problems.

(2) Derivative pricing: Structured products; Path-dependent options; Derivative securities; Asset pricing models; Robust Pricing; Price theory and market structure; Risk theory; Corporate debts and pricing beyond Black-Scholes model; Price of risk.

(3) Risk measures and risk management in finance markets: Risk measures; Distortion risk measures; Portfolio Selection under ambiguity aversion; Robust portfolio management.


Selected Publications


1.    Zongxia Liang, Ming Ma. Robust consumption-investment problem under CRRA and CARA utilities with time-varying confidence sets. Accepted for publication in Mathematical Finance. (pdf)

2.     Lin He, Zongxia Liang, Yang Liu and Ming Ma. Optimal control of DC pension plan management under two incentive schemes. Published online in North American Actuarial Journal. (pdf)

3.     Zongxia Liang, Ming Ma. Consumption-investment problem with pathwise ambiguity under logarithmic utility. Accepted for publication in Mathematics and Financial Economics .(pdf)

4.     Guohui Guan, Zongxia Liang, Jian Feng. Time-consistent proportional reinsurance and investment strategies under ambiguous environment. Insurance: Mathematics and Economics 83(2018)122-133 (pdf)

5. Lin He, Zongxia Liang and Xiaoyang Zhao. Tunneling behaviors of two mutual funds. Journal of Industrial and Management Optimization 14(4)(2018)1617-1649. (pdf)

6.Zongxia Liang and Xiaoyang Zhao. Optimal mean-variance efficiency of a family with life insurance under inflation risk, Insurance: Mathematics and Economics 71(2016)164-178(pdf)). 

7.Guohui Guan, Zongxia Liang. A stochastic Nash equilibrium portfolio game between two DC pension funds, Insurance: Mathematics and Economics70(2016)237-244(pdf).

8.Guohui Guan, Zongxia Liang. Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints, Insurance :Mathematics and Economics 69(2016) 224-237(pdf)

9. Zongxia Liang and Wenlong Sheng. Valuing inflation-linked death benefits under a stochastic volatility framework, Insurance: Mathematics and Economics 69 (2016) 45-58(pdf).

10. Zongxia Liang and Mingsi Long. Minimization of absolute ruin probability under negative correlation assumption, Insurance: Mathematics and Economics 65 (2015) 247-258(pdf).

11. Zongxia Liang and Min Song. Time-consistent reinsurance and investment strategies for mean-variance insurer under partial information. Insurance: Mathematics and Economics 65 (2015)66-76 (pdf).

12. Zongxia Liang and Ming Ma. Optimal dynamic asset allocation of pension fund in mortality and salary risks framework. Insurance: Mathematics and Economics 64(2015)151-161(pdf).

13. Lin He, Zongxia Liang. Optimal assets allocation and benefit outgo policies of DC pension plan with compulsory conversion claims. Insurance: Mathematics and Economics Vol.61, pp 227-234(2015) (pdf)

14. Guohui Guan, Zongxia Liang. Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns. Insurance: Mathematics and Economics Vol.61, pp99-109(2015) (pdf).

15. Guohui Guan, Zongxia Liang. Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insurance: Mathematics and Economics Vol.57, pp58-66(2014) (pdf).

16. Guohui Guan, Zongxia Liang. Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks. Insurance: Mathematics and Economics, Vol.55, pp105-115(2014(pdf).

17. Huiqi Guan, Zongxia Liang. Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs. Insurance: Mathematics and Economics, Vol.54, pp109-122(2014) (pdf).

18. Lin He, Zongxia Liang. Optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework. Insurance: Mathematics and Economics, Vol.53, No.3, pp643-649(2013) (pdf).

19. Lin He, Zongxia Liang. Optimal dynamic asset allocation Strategy for ELA scheme of DC pension plan during the distribution phase. Insurance: Mathematics and Economics, Vol.52, No.2, pp404-410(2013)( pdf ).

20. Zongxia Liang, Weiming Wu. Variational inequalities in stock loan models. Optimization and Engineering, Vol.13 (3), pp459-470, 2012 (pdf).

21. Zongxia Liang, Jianping Huang. Optimal dividend and investing control of an insurance company with higher solvency constraints. Insurance: Mathematics and Economics, Vol. 49, pp501-511, 2011(pdf).

22. Zongxia Liang, Bin Sun. Optimal control of a big financial company with debt liability under bankrupt probability constraints. Frontiers of Mathematics in China, Vol.6, No.6, 1095-1130, 2011( pdf ).

23. Zongxia Liang, Weiming Wu, Shuqing Jiang. Stock loan with automatic termination clause, cap and margin. Computers and Mathematics with Applications, Vol. 60, pp3160–3176, 2010 ( pdf ).

24. Lin He, Zongxia Liang. Intertemporal Capital Asset Pricing Model for the Insider. The 9th International Conference on Information and Management Science, 2010( pdf )

25. Lin He, Zongxia Liang. Optimal Financing and Dividend Control of the Insurance Company with Fixed and Proportional Transaction Costs. Insurance: Mathematics and Economics, Vol. 44, pp 88-94, 2009( pdf ).

26. Zongxia Liang. Karhunen-Loeve Expansion for stochastic convolution of cylindrical fractional Brownian motions. Recent Development in Stochastic Dynamics and Stochastic Analysis.

Interdisciplinary Mathematical Sciences, Vol.8, 2009, pp195-206(pdf).

27. Lin He, Zongxia Liang, Fei Xing. The Influence of Transaction Costs on Optimal Control for an Insurance Company with a New Value Function. Recent Development in Stochastic Dynamics and Stochastic Analysis. Interdisciplinary Mathematical Sciences, Vol. 8, 2009, pp. 143-160(pdf)

28. Lin He, Ping Hou, Zongxia Liang. Optimal Control of the Insurance Company with Proportional Reinsurance Policy under Solvency Constraints. Insurance: Mathematics and Economics, Vol.43, pp474-479, 2008 ( pdf ).

29. Lin He, Zongxia Liang. Optimal Financing and Dividend Control of the Insurance Company with Proportional Reinsurance Policy. Insurance: Mathematics and Economics, Vol. 42, pp 976-983, 2008(pdf ) .

30. Zongxia Liang. Anticipating multidimensional stochastic differential equations with reflections. Stochastics and Dynamics, 2008, Vol8, No.2, pp 295-318(pdf).

31. Zongxia Liang. Spatial asymptotic behavior of homeomorphic global flows for non-Lipschitz SDEs. Bulletin Des Sciences Mathematiques, 2008, Vol. 132, No.2, pp146-163(pdf).

32. Lin He, Zongxia Liang. The Influence of Bankruptcy Value on Optimal Control for Insurance Company with a New Value Function. The 7th International Conference on Information and Management Science, 2008 (pdf).

33. Zongxia Liang. Besov Regularity for the Generalized Local Time of the Indefinite Skorohod Integral. Ann.Inst.Henri Poincaré(B) Probab.Stat. 43(2007), no.1,77-86(pdf).

34. Zongxia Liang. Stochastic differential equations driven by spatial parameters semimartingale with non-Lischitz local characteristic. Potential Analysis, 2007, Vol. 26, No.4, 307-322( pdf ).

35. Guilan Cao, Kai He, Zongxia Liang. Quasi sure analysis of local times of anticipating smooth semimartingales. Bulletin Des Sciences Mathematiques, 2007, Vol.131, No.8, 697-715 (pdf).

36. Zongxia Liang. Kunita-type stochastic flows of homeomorphisms in Euclidean space. Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol.10, No.4(2007)1-16(pdf).

37. Zongxia Liang. Fractional smoothness for the generalized local time of the indefinite skorohod integral. Journal of Functional Analysis, 2006, Vol.239, No.1,247-267(pdf) .

38. Zongxia Liang. Stochastic Differential Equation Driven by Countably Many Brownian Motions with Non-Lipschitzian Coefficients. Stochastic Analysis and Applications, 2006, Vol. 24, No.3, 501-529(pdf).

39. Zongxia Liang. Anticipative Stochastic differential Equations with non- smooth diffusion coefficient. Acta Mathematica Sinica, 2006, Vol.22, No.5, 1473-1480(pdf).

40. Zongxia Liang. Homeomorphic property of solutions of SDE driven by countably many Brownian motions with non-Lipschitzian coefficients. Bulletin Des Sciences Mathematiques, 2005, Vol.129, No.6, 523-538(pdf).

41. Zongxia Liang. Exit Problems for Nonlinear Stochastic Evolution Equations on Hilbert Spaces. Sciences in China, 2002, Vol.45, No.10, 1238-1254(pdf).

42. Zongxia Liang, Xiaoyang Zhao. Optimal investment, consumption and life insurance under stochastic framework (in Chinese). Sci Sin Math, 2016, 46: 1863–1882, doi: 10.1360/012016-28 (pdf).

43. Lin He, Zongxia Liang. Optimal pension decision under heterogenous health statuses and bequest motives . Journal of Industrial and Management Optimization.13(4)( 2017)1641-1659.(pdf).

44. Zongxia Liang. Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane. Stochastic Processes and Their Applications, 83(2): 303-317, 1999(pdf).

45. Zongxia Liang. Uniqueness theorem of solutions for stochastic differential equation in the plane. Acta Mathematica Sinica, 14(4), pp495-506, 1998(pdf).

46. Zongxia Liang, Mingli Zheng. Exponential integrability, exponential decay of entropy and logarithmic Sobolev inequalities of symmetric diffusions. Math. Appl.11 (1998) 9-13 (pdf)

47. Zongxia Liang. Two parameter smooth martingales on the Wiener space. Acta Mathematica Sinica, 13(1997), no.2, 239-246 (pdf).

48. Zongxia Liang, Mingli Zheng. Existence, pathwise uniqueness and convergence of solutions to two-parameter linear integrodifferential martingale stochastic equations. Math. Appl. 10(4), pp33-38, 1997 (pdf)

49. Zongxia Liang. Quasi Sure quadratic variations of two parameter smooth martingales on the Wiener space. Journal of Mathematics of Kyoto University, 36 (3):619-640,1996 (pdf).

50. Zongxia Liang, Zheng ML. Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane. Stochastic Processes and Their Applications, 62 (2): 263-276, 1996 (pdf).


Working papers


1.    Guohui Guan, Zongxia Liang. Robust optimal reinsurance and investment strategies for an AAI with multiple risks.

2.    Lin He, Zongxia Liang, Yang Liu and Ming Ma. Weighted Utility Optimization of the Participating Annuity Contract.

3.    Zongxia Liang, Yang Liu. Weighted utility optimization problem in the hedge fund.


主要研究课题

国家自然科学基金资助课题等


Teaching


Courses for undergraduate students:

Probability Theory(I); Probability Theory and Mathematical Statistics; Stochastic Mathematics; Calculus; Mathematical Analysis; Complex Analysis.

Courses for graduate students:

Probability Theory (II); Measure Theory; Modern Actuarial Risk Theory; Advanced Probability Theory; Stochastic Processes; Stochastic Analysis; Stochastic Calculus; Mathematical Finance; Risk Theory; Topics in Stochastic Analysis.


招生

1.每年招收博士研究生两名。

2.招生学科:数学和统计学。

3.研究方向:

A.Probability Theory, Stochastic Analysis and Stochastic controls.

B. Insurance Mathematics and Actuarial Science.

C. Mathematical Finance, Financial Engineering and Financial Economics.


主要连接


1http://www.ams.org/home/page

2http://www.ams.org/mathscinet/

3http://arxiv.org/

4http://www.math.nus.edu.sg/~matdm/papers.htm

5http://www.cms.org.cn/cms/index.htm

6http://www.nsfc.gov.cn/Portal0/default124.htm

7. http://www.math.columbia.edu/~ik/publications.html

8. http://sas.uwaterloo.ca/~wang/publications.html


教学使用教材



春季数学系本科生(二年级下学期)概率论(I)教学使用教材

1.概率论,杨振明编,科学出版社。

2.A Course in Probability Theory, Kai Lai Chung(pdf).

3.(参考书)Probability Theory and Examples, Third Edition, Richard Durrett. ISBN: 0-534-42441-4(pdf).

4. (参考书) 概率论教程, 缪柏其,胡太忠, 编著,中国科技大学出版社.


秋季数学系随机分析(4学分,适用于高年级本科生, 学术型硕士研究生和博士研究生)教学使用教材

1.    Brownian Motion and Stochastic Calculus(pdf).

2.      Stochastic Differential Equations(pdf).


 


数学系概率论方面课程教学内容(大纲)描述:

1.    Probability Theory(I)(春季)(pdf).

2.    Applied Stochastic Processes(秋季)(pdf).

3.    Probability Theory(II)(秋季)(pdf).

4.    Stochastic Processes(春季)(pdf).

5.    Stochastic Analysis(秋季)(pdf).

6.    Advanced Probability Theory(春季)(pdf).