一. 学术研究成果
(1)在金融数学的国际顶级或一流学术期刊如:Mathematical Finance (MF), Finance and Stochastics (FS), SIAM Journal on Financial Mathematics(SIFIN), Quantitative Finance (QF), Mathematics and Financial Economics (MFE); 精算科学领域的国际四大核心学术期刊如:Insurance:Mathematics and Economics（IME), Scandinavian Actuarial Journal (SAJ), North American Actuarial Journal (NAAJ); 分析与概率论领域的国际顶级或一流学术期刊如:Journal of Functional Analysis(JFA), Stochastic Processes and their Applications(SPA), Ann.Inst.Henri Poincare Probab.Statist., Advances in Applied Probability; 运筹学,控制论与优化领域的国际顶级或一流学术期刊如：Mathematics of Operations Research (MOR)，SIAM Journal on Control and Optimization (SICON), European Journal of Operational Research (EJOR)等杂志上发表论文八十余篇.
(2) 在金融数学,精算科学,概率论,随机控制与优化及其交叉领域提出了原创性概念及其挑战性数学问题,做出了系列原创性和创新性基础研究成果.(a) 解决了不完备模糊金融市场中关于最优投资组合与消费的众知数学猜想问题,建立了非可控型随机稳健控制与优化理论;(b) 提出了最优停时与随机控制混合型弱均衡概念,建立相应理论体系同时提出了相应扩展型HJBE系统的挑战性数学问题;(c)系统建立了隐式框架下投资组合均衡理论;(d) 率先严格建立不完备金融市场中光滑模糊数学概念与框架,解决了著名的KMM问题,发展了光滑模糊均衡投资组合理论;(e) 率先解决了不完备金融市场中MMV下的最优投资组合及最优再保险的随机控制问题,拓展改进了MV理论;(f) 提出构造解决高度非凸(凹)非线性随机最优控制与优化问题的新方法;(g) 在精算科学领域率先引入局部时过程及其相应动态随机控制等概念,系统严格建立动态分红,再保险,投资,DC(DB)养老金管理与投资方面的(稳健)随机控制与优化理论,给出了研究这些控制问题系列新方法与工具,解决了系列前沿问题,推进了精算科学与风险管理发展的进程;(h) 首次解决了双曲鞅型SPDE适定性问题,系统详细研究了两参数鞅过程和局部时过程轨道的拟必然性质和正则性。
(3)在精算科学研究领域,梁宗霞教授及其研究团队的研究位于世界前列,取得了清华大学精算科学最新四个5年周期(2012-2016, 2013-2017, 2014-2018,2015-2019)世界非商学院类排名中分别世界排名第三,第五,第六,第八,大陆高校及研究机构排名第一的研究成果.见 https://business.unl.edu/academic-programs/departments/finance/actuarial-science/research-rankings
二. Selected Publications:
[69] Guohui Guan, Zongxia Liang，Jianming Xia. Equilibrium portfolio selection for smooth ambiguity preferences. Mathematics of Operations Research. Published Online: April 24, 2024.
[68] Yuchen Li, Zongxia Liang, Shunzhi Pang. Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model. Mathematics of Operations Research. Published Online:September 23, 2024.
[67] Zongxia Liang， Xiaodong Luo, Fengyi Yuan. Equilibria for Time-Inconsistent Singular Control Problems. SIAM Journal on Control and Optimization. Forthcoming.
[66] Zongxia Liang, Keyu Zhang. Time-inconsistent mean field and n-agent games under relative performance criteria. SIAM Journal on Financial Mathematics. Forthcoming.
[65] Lin He, Zongxia Liang, Zhaojie Ren. Optimal consumption and investment in pooled annuity funds with and without fund managers. Scandinavian Actuarial Journal, Published online: 15 Aug 2024.
[64] Zongxia Liang,Yang Liu, Litian Zhang. A Framework of State-dependent Utility Optimization with General Benchmarks. Finance and Stochastics, Forthcoming.
[63] Zongxia Liang, Keyu Zhang. A Mean field game approach to relative investment-consumption games with habit formation. Mathematics and Financial Economics, Published: 02 May 2024,
[62] Zongxia Liang,Yang Liu, Ming Ma and Rahul Pothi Vinoth. A unified formula of the optimal portfolio for piecewise hyperbolic absolute risk aversion utilities. Quantitative Finance 24(2)(2024)281-303,
[61] Zongxia Liang, Xia Yi, Bin Zou. A two-layer stochastic game approach to reinsurance contracting and competition. Insurance: Mathematics and Economics 119(2024)226-237.
[60] Guohui Guan, Zongxia Liang and Xingjian Ma. Optimal annuitization and asset allocation under linear habit formation, Insurance: Mathematics and Economics 114(1)(2024)176-191.
[59] Guohui Guan, Zongxia Liang and Yi Xia. Optimal management of DB pension fund under both underfunded and overfunded cases, Scandinavian Actuarial Journal 2024(6)(2024) 583-624.
[58] Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song. Optimal mix among PAYGO, EET and individual savings. Scandinavian Actuarial Journal 2024(5)(2024)463-505.
[57] Zongxia Liang and Fengyi Yuan. Weak equilibria for time-inconsistent control. With applications to investment-withdrawal decisions. Mathematical Finance 33(3) (2023) 891-945.
[56] Guohui Guan, Zongxia Liang and Yi Xia. Optimal management of DC pension fund under the relative performance ratio and VaR constraint. European Journal of Operational Research 305(2)(2023)868-886.
[55] Zongxia Liang, Xiaodong Luo and Fengyi Yuan. Consumption-investment decisions with endogenous reference point and drawdown constraint. Mathematics and Financial Economics 17(2)(2023)285-334.
[54] Guohui Guan, Lin He, Zongxia Liang, Yang Liu and Litian Zhang. Robust dividend, financing, and reinsurance strategies under model uncertainty with proportional transaction costs. North American Actuarial Journal 28(2)(2024)261-284.
[53] Guohui Guan, Zongxia Liang, Yilun Song. A Stackelberg reinsurance-investment game under α-maxmin mean-variance criterion and stochastic volatility. Scandinavian Actuarial Journal, 2024(1)(2024)28-63.
[52] Zongxia Liang and Yang Liu. An asymptotic approach to centrally-planned portfolio selection. Advances in Applied Probability 56(3)(2024)757-784.
[51] Guohui Guan, Jiaqi Hu and Zongxia Liang. Robust equilibrium strategies in a defined benefit pension plan game. Insurance: Mathematics and Economics 106(2022)193-217.
[50] Lin He, Zongxia Liang and Sheng Wang. Dynamic optimal adjustment policies of hybrid pension plans. Insurance: Mathematics and Economics 106 (2022) 46–68.
[49] Lin He, Zongxia Liang, Yilun Song and Qi Ye. Optimal asset allocation, consumption and retirement time with the variation in habitual persistence. Insurance: Mathematics and Economics 102 (2022)188–202.
[48] Lin He, Zongxia Liang, Yilun Song and Qi Ye. Optimal contribution rate of PAYGO pension. Scandinavian Actuarial Journal, 2021, 2021(6), 505–531.
[47] Zongxia Liang and Yang Liu. A classification approach to general S-shaped utility optimization with principals' constraints. SIAM Journal on Control and Optimization 58(6)(2020)3734-3762.
[46] Zongxia Liang and Ming Ma. Robust consumption-investment problem under CRRA and CARA utilities with time-varying confidence sets. Mathematical Finance 30(2020)1035-1072.
[45] Lin He, Zongxia Liang and Fengyi Yuan. Optimal DB-PAYGO pension management towards a habitual contribution rate. Insurance:Mathematics and Economics 94(2020)125-141.
[44] Lin He, Zongxia Liang, Yang Liu and Ming Ma. Weighted utility optimization of the participating endowment contract. Scandinavian Actuarial Journal.2020, 2020(7), 577-613.
[43] Guohui Guan, Zongxia Liang. Robust optimal reinsurance and investment strategies for an AAI with multiple risks. Insurance:Mathematics and Economics 89(2019)63-78.
[42] Zongxia Liang, Ming Ma. Consumption-investment problem with pathwise ambiguity under logarithmic utility. Mathematics and Financial Economics 13(4)(2019)519-541.
[41] Lin He, Zongxia Liang, Yang Liu and Ming Ma. Optimal control of DC pension plan management under two incentive schemes. North American Actuarial Journal 23(1)(2019)120-141.
[40] Guohui Guan, Zongxia Liang and Jian Feng. Time-consistent proportional reinsurance and investment strategies under ambiguous environment. Insurance:Mathematics and Economics 83(2018)122-133.
[39] Lin He, Zongxia Liang, Xiaoyang Zhao. Tunneling behaviors of two mutual funds. Journal of Industrial and Management Optimization. 14(4)( 2018) 1617-1649.
[38] Lin He, Zongxia Liang. Optimal pension decision under heterogeneous health statuses and bequest motives. Journal of Industrial and Management Optimization. 13(4)(2017) 1641-1659.
[37] Zongxia Liang, Xiaoyang Zhao. Optimal mean-variance efficiency of a family with life insurance under inflation risk. Insurance:Mathematics and Economics 71(2016)164-178.
[36] Zongxia Liang, Xiaoyang Zhao. Optimal investment, consumption and life insurance under stochastic framework. SCIENTIA SINICA Mathematica. 46(12)(2016)1863-1882.
[35] Guohui Guan, Zongxia Liang. A stochastic Nash equilibrium portfolio game between two DC pension funds. Insurance:Mathematics and Economics 70(2016) 237-244.
[34] 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.
[33] Zongxia Liang, Wenlong Sheng. Valuing inflation-linked death benefits under a stochastic volatility framework. Insurance:Mathematics and Economics 69(2016)45-58.
[32] Zongxia Liang, Mingsi Long. Minimization of absolute ruin probability under negative correlation assumption. Insurance:Mathematics and Economics 65(2015) 247-258.
[31] Zongxia Liang, Min Song. Time-consistent reinsurance and investment strategies for mean-variance insurer under partial information. Insurance:Mathematics and Economics 65(2015)66-76.
[30] Zongxia Liang, Ming Ma. Optimal dynamic asset allocation of pension fund in mortality and salary risks framework. Insurance:Mathematics and Economics 64(2015)151-161.
[29] Lin He, Zongxia Liang. Optimal assets allocation and benefit outgo policies of DC pension plan with compulsory conversion claims. Insurance:Mathematics and Economics 61(2015)227-234.
[28] Guohui Guan, Zongxia Liang. Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns. Insurance:Mathematics and Economics 61(2015)99-109.
[27] Guohui Guan, Zongxia Liang. Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insurance:Mathematics and Economics 57(2014)58-66.
[26] Guohui Guan, Zongxia Liang. Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks. Insurance:Mathematics and Economics 55(2014)105-115.
[25] Huiqi Guan, Zongxia Liang. Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs. Insurance:Mathematics and Economics 54(2014)109-122.
[24] 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 53(2013)643-649.
[23] Lin He, Zongxia Liang. Optimal dynamic asset allocation strategy for ELA scheme of DC pension plan during the distribution phase. Insurance:Mathematics and Economics 52(2013)404-410.
[22] Zongxia Liang, Weiming Wu. Variational inequalities in stock loan models. Optimization and Engineering 13(3)(2012)459-470.
[21] Zongxia Liang, Jianping Huang. Optimal dividend and investing control of an insurance company with higher solvency constraints. Insurance:Mathematics and Economics 49(2011)501-511.
[20] Zongxia Liang, Bin Sun. Optimal control of a big financial company with debt liability under bankrupt probability constraints. Front. Math. China. 6(6)(2011)1095-1130.
[19] Zongxia Liang, Weiming Wu and Shuqing Jiang. Stock loan with automatic termination clause, cap and margin. Computers and Mathematics with Applications 60(12)(2010)3160-3176.
[18] Lin He, Zongxia Liang. Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs. Insurance: Mathematics and Economics 44(2009)88-94.
[17] Lin He, Ping Hou and Zongxia Liang. Optimal control of the insurance company with proportional reinsurance policy under solvency constraints. Insurance: Mathematics and Economics 43(2008)474-479.
[16] Lin He, Zongxia Liang. Optimal financing and dividend control of the insurance company with proportional reinsurance policy. Insurance:Mathematics and Economics 42(2008)976-983.
[15] Zongxia Liang. Anticipating multidimensional stochastic differential equations with reflections. Stochastics and Dynamics 8(2)(2008)295-318.
[14] Zongxia Liang. Spatial asymptotic behavior of homeomorphic global flow for non-Lipschitz SDEs. Bulletin des Sciences Mathématiques 132(2)(2008)146-163.
[13] Guilan Cao, Kai He and Zongxia Liang. Quasi sure analysis of local times of anticipating smooth semimartingales. Bulletin des Sciences Mathématiques 131(8)(2007)697-715.
[12] Zongxia Liang. Stochastic differential equations driven by spatial parameters semimartingale with non-Lipschitz local characteristic. Potential Analysis(4)(2007)307-322.
[11] Zongxia Liang. Besov regularity for the generalized local time of the indefinite Skorohod integral. Annales de l'Institut Henri Poincaré Probabilités et Statistiques 43(1)(2007)77-86.
[10] Zongxia Liang. Fractional smoothness for the generalized local time of the Indefinite Skorohod integral. Journal of Functional Analysis 239(1)(2006)247-267.
[9] Zongxia Liang. Anticipative stochastic differential equations with non-smooth diffusion coefficient. Acta Math. Sin. 22(5)(2006)1473–1480.
[8] Zongxia Liang. Stochastic differential equation driven by countably many Brownian motions with non-Lipschitzian coefficients. Stochastic Analysis and Applications 24(3)(2006)501-529.
[7] Zongxia Liang. Homeomorphic property of solutions of SDE driven by countably many Brownian motions with non-Lipschitzian coefficients. Bulletin des Sciences Mathématiques 129(6)(2005)523-538.
[6] Zongxia Liang. Exit problems for nonlinear stochastic evolution equations on Hilbert spaces. Science in China. Series A. Mathematics 45(10)(2002)1238-1254.
[5] Zongxia Liang.Existen ce and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane. Stochastic Processes and their Applications 83(2)(1999)303-317.
[4] Zongxia Liang. Uniqueness theorem of solutions for stochastic differential equation in the plane. Acta Math. Sin.14(4)(1998) 495–506.
[3] Zongxia Liang.Two parameter smooth martingales on the Wiener space. Acta Math. Sin.13(2)(1997) 239–246.
[2] Zongxia Liang. Quasi-sure quadratic variations of two parameter smooth martingales on the Wiener space. Journal of Mathematics of Kyoto University 36(3)(1996)619-640.
[1] Zongxia Liang, Mingli Zheng. Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane.Stochastic Processes and their Applications 62(2)(1996)263-276.
三. Selected Articles in arXiv:
1. arXiv:2410.18432
Dynamic Investment-Driven Insurance Pricing: Equilibrium Analysis and Welfare Implication
Authors: Bingzheng Chen, Zongxia Liang, Shunzhi Pang
2. arXiv:2410.16621
Equilibrium portfolio selection under beliefs-dependent utilities
Authors: Xiaochen Chen, Guohui Guan, Zongxia Liang
3. arXiv:2409.19571
Robust Portfolio Selection under State-dependent Confidence Set
Authors: Guohui Guan, Yuting Jia, Zongxia Liang
4. arXiv:2409.07219
On time-inconsistent extended mean-field control problems with common noise
Authors: Zongxia Liang, Xiang Yu, Keyu Zhang
5. arXiv:2403.13388
Optimal VPPI strategy under Omega ratio with stochastic benchmark
Authors: Guohui Guan, Lin He, Zongxia Liang, Litian Zhang
6. arXiv:2403.06190
Monotone Mean-Variance Portfolio Selection in Semimartingale Markets: Martingale Method
Authors: Yuchen Li, Zongxia Liang, Shunzhi Pang
7. arXiv:2402.11580
Stackelberg reinsurance and premium decisions with MV criterion and irreversibility
Authors: Zongxia Liang, Xiaodong Luo
8. arXiv:2401.08323
Dynamic portfolio selection under generalized disappointment aversion
Authors: Zongxia Liang, Sheng Wang, Jianming Xia, Fengyi Yuan
9. arXiv:2312.15173
Equilibrium stochastic control with implicitly defined objective functions
Authors: Zongxia Liang, Jianming Xia, Keyu Zhang
10. arXiv:2312.14437
Time-inconsistent mean field and n-agent games under relative performance criteria
Authors: Zongxia Liang, Keyu Zhang
11. arXiv:2311.06745
Dynamic portfolio selection for nonlinear law-dependent preferences
Authors: Zongxia Liang, Jianming Xia, Fengyi Yuan
12. arXiv:2310.09198
Equilibria for Time-inconsistent Singular Control Problems
Authors: Zongxia Liang, Xiaodong Luo, Fengyi Yuan
13. arXiv:2302.09218
Optimal Mix Among PAYGO, EET and Individual Savings
Authors: Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song
14. arXiv:2302.08731
Optimal management of DB pension fund under both underfunded and overfunded cases
Authors: Guohui Guan, Zongxia Liang, Yi Xia
15. arXiv:2302.08181
Equilibrium Portfolio Selection for Smooth Ambiguity Preferences
Authors: Guohui Guan, Zongxia Liang, Jianming Xia
16. arXiv:2212.14327
A Stackelberg reinsurance-investment game under α-maxmin mean-variance criterion and stochastic volatility
Authors: Guohui Guan, Zongxia Liang, Yilun Song
17. arXiv:2211.14473
Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model
Authors: Yuchen Li, Zongxia Liang, Shunzhi Pang
18. arXiv:2211.12168
Continuous-Time Monotone Mean-Variance Portfolio Selection in Jump-Diffusion Model
Authors: Yuchen Li, Zongxia Liang, Shunzhi Pang
Submitted 10 May, 2024; v1 submitted 22 November, 2022; originally announced November 2022.
19. arXiv:2210.13833
The continuous-time pre-commitment KMM problem in incomplete markets
Authors: Guohui Guan, Zongxia Liang, Yilun Song
20. arXiv:2209.09709 [pdf, other]
Modern Tontine with Transaction Costs
Authors: Lin He, Zongxia Liang, Sheng Wang
