清華大學數學科學系長聘教授,博士生導師,博士(中國科學院套用數學所,1996).
基本介紹
- 中文名：梁宗霞
- 畢業院校：北京大學
基本信息,工作履歷,研究領域,獎勵與榮譽,學術成果,
基本信息
清華大學數學科學系長聘教授,博士生導師,博士(中國科學院套用數學所,1996).
工作履歷
1998-目前,清華大學數學科學系,講師,副教授,教授
1996-1998, 北京大學數學科學學院機率統計系,博士後
2008.09-2009.08, 韓國國立首爾大學(SNU), 客座研究員
2002.09-2003.11, 美國麻省理工學院(MIT)數學系,客座研究員
研究領域
精算科學,金融數學(數理金融),機率論與隨機分析, 隨機最優控制與最佳化,風險管理與保險數學,數理經濟學,強化學習理論
獎勵與榮譽
1.主持一項國家自然科學基金委青年基金項目及五項國家自然科學基金委面上項目,...
2.2019年,2021年及2024年清華大學優秀博士學位論文指導教師,2010年度清華大學優秀碩士學位論文指導教師
學術成果
一. 學術研究成果
(1)在金融數學領域的國際頂級或一流學術期刊如:Mathematical Finance (MF), Finance and Stochastics (FS), SIAM Journal on Financial Mathematics(SIFIN), Quantitative Finance (QF), Mathematics and Financial Economics (MFE); 精算科學領域的國際四大核心學術期刊如:Insurance:Mathematics and Economics（IME）, Scandinavian Actuarial Journal (SAJ), North American Actuarial Journal (NAAJ); 機率論與分析領域的國際頂級或一流學術期刊如: Annals of Applied Probability, Stochastic Processes and their Applications(SPA), Ann.Inst.Henri Poincare Probab.Statist., Journal of Functional Analysis(JFA), Advances in Applied Probability; 運籌學,控制論與最佳化領域的國際頂級或一流學術期刊如：Mathematics of Operations Research (MOR), SIAM Journal on Control and Optimization (SICON), Annals of Operations Research(AOR), European Journal of Operational Research (EJOR)等雜誌上發表論文九十餘篇.
(2) 在金融數學,精算科學,機率論,隨機控制與最佳化及其交叉領域提出了原創性概念及其挑戰性數學問題,做出了系列原創性和創新性基礎研究成果.(a) 解決了不完備模糊金融市場中關於最優投資組合與消費的眾知數學猜想問題,建立了非可控型隨機穩健控制與最佳化理論;(b) 提出了最優停時與隨機控制混合型弱均衡概念,建立相應理論體系同時提出了相應擴展型 Hamilton-Jacobi-Bellman系統的挑戰性數學問題;(c)系統建立了隱式框架下投資組合均衡理論;(d)率先嚴格建立不完備金融市場中光滑模糊數學概念與框架,解決了著名的KMM問題,發展了光滑模糊均衡投資組合理論;(e) 率先解決了不完備金融市場中MMV下的最優投資組合及最優再保險的隨機控制問題,拓展改進了MV理論;(f) 提出構造解決高度非凸(凹)非線性隨機最優控制與最佳化問題的新方法;(g)在精算科學領域率先引入局部時過程及其相應動態隨機控制等概念,系統嚴格建立動態分紅,再保險,投資,DC(DB)養老金管理與投資方面的(穩健)隨機控制與最佳化理論,給出了研究這些控制問題系列新方法與工具,解決了系列前沿問題,推進了精算科學與風險管理髮展的進程;(h)首次解決了雙曲鞅型SPDE適定性問題,系統詳細研究了兩參數鞅過程和局部時過程軌道的擬必然性質和正則性。
(3)在精算科學研究領域,梁宗霞教授和他的學生研究團隊的研究位於世界前列,取得了清華大學精算科學最新四個5年周期(2012-2016, 2013-2017, 2014-2018,2015-2019)世界非商學院類排名中分別世界排名第三,第五,第六,第八,大陸高校及研究機構排名第一的研究成果.
二. Selected Publications
[79] Xiaochen Chen, Guohui Guan, Zongxia Liang. Equilibrium portfolio selection under beliefs-dependent utilities. Mathematics of Operations Research. Forthcoming.
[78] Lin He, Yuting Jia, Zongxia Liang, Sheng Wang. Dynamic optimal adjustment policies of hybrid pension plans under habitual persistence. Mathematics and Financial Economics. Published online: 13 Aug 2025 .
[77] Guohui Guan, Zongxia Liang. N-agentheterogeneous investment-consumption game underα-maxmin mean-variance utility criterion. Journal of Optimization Theory and Applications. Forthcoming.
[76] Guohui Guan, Zongxia Liang and Yilun Song. The continuous-time pre-commitment KMM problem in incomplete markets. Annals of Applied Probability 35(4)(2025) 2923-2966.
[75] Zongxia Liang，Jianming Xia and Fengyi Yuan. Dynamic portfolio selection for nonlinear law-dependent preferences. Mathematics of Operations Research. Published Online: Jun 30, 2025.
[74] Guohui Guan, Zongxia Liang and Yi Xia. Robust meanvariance stochastic differential reinsurance and investment games under volatility risk and model uncertainty. Scandinavian Actuarial Journal. Published online: 20 May 2025.
[73] Guohui Guan, Qitao Huang, Zongxia Liang, Fengyi Yuan. Retirement decision with addictive habit persistence in a jump diffusion market. SIAM Journal on Financial Mathematics 16(3)(2025)912-958
[72] Guohui Guan, Zongxia Liang and Yi Xia. Many insurer robust games of reinsurance and investment under model uncertainty in incomplete markets. Mathematics and Financial Economics. Published Online: July 1, 2025.
[71] Zongxia Liang,Yang Liu, Litian Zhang. A framework of state-dependent utility optimization with general benchmarks.
Finance and Stochastics 29(2)(2025)469-518.
[70] Guohui Guan, Jiaqi Hu, Zongxia Liang. N-player and mean field games among fund managers considering excess logarithmic returns. Annals of Operations Research 349(2025)1663-1691.
[69] Guohui Guan, Zongxia Liang, Jianming Xia. Equilibrium portfolio selection for smooth ambiguity preferences.
Mathematics of Operations Research 50(2)(2025) 1042–1071.
[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 50(3)(2025):2405-2432.
[67] Yuchen Li, Zongxia Liang, Shunzhi Pang. Comparison between mean-variance and monotone mean-variance preferences in general markets: A new perspective. Operations Research Letters 61 (2025) 107298.
[66] Zongxia Liang, Xiaodong Luo. Stackelberg reinsurance and premium decisions with MV criterion and irreversibility. SIAM Journal on Financial Mathematics 16(1)(2025)167-199.
[65] Zongxia Liang, Sheng Wang, Jianming Xia. An integral equation in portfolio selection with time-inconsistent preferences. SIAM Journal on Financial Mathematics 16(1)(2025) SC12-SC23.
[64] Lin He, Zongxia Liang, Zhaojie Ren. Optimal consumption and investment in pooled annuity funds with and without fund managers. Scandinavian Actuarial Journal 2025(1)(2025)79-116.
[63] Zongxia Liang, Xiaodong Luo, Fengyi Yuan. Equilibria for time-inconsistent singular control problems. SIAM Journal on Control and Optimization 62(6)(2024) 3213-3238.
[62] Zongxia Liang, Keyu Zhang. Time-inconsistent mean field and n-agent games under relative performance criteria. SIAM Journal on Financial Mathematics 15(4)(2024)1047-1082.
[61] Zongxia Liang, Keyu Zhang. A Mean field game approach to relative investment-consumption games with habit formation. Mathematics and Financial Economics 18(4)(2024)577-622.
[60] 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.
[59] 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.
[58] 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.
[57] 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.
[56] Lin He, Zongxia Liang, Zhaojie Ren, Yilun Song. Optimal mix among PAYGO, EET and individual savings. Scandinavian Actuarial Journal 2024(5)(2024)463-505.
[55] 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.
[54] 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.
[53] Zongxia Liang and Yang Liu. An asymptotic approach to centrally-planned portfolio selection. Advances in Applied Probability 56(3)(2024)757-784.
[52] Zongxia Liang and Fengyi Yuan. Weak equilibria for time-inconsistent control. With applications to investment-withdrawal decisions. Mathematical Finance 33(3) (2023) 891-945.
[51] 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.
[50] 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.
[49] 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.
[48] Lin He, Zongxia Liang and Sheng Wang. Dynamic optimal adjustment policies of hybrid pension plans. Insurance: Mathematics and Economics 106 (2022) 46–68.
[47] 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.
[46] Lin He, Zongxia Liang, Yilun Song and Qi Ye. Optimal contribution rate of PAYGO pension. Scandinavian Actuarial Journal 2021, 2021(6), 505–531.
[45] 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.
[44] 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.
[43] 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.
[42] 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.
[41] Guohui Guan, Zongxia Liang. Robust optimal reinsurance and investment strategies for an AAI with multiple risks. Insurance:Mathematics and Economics 89(2019)63-78
[40] Zongxia Liang, Ming Ma. Consumption-investment problem with pathwise ambiguity under logarithmic utility. Mathematics and Financial Economics 13(4)(2019)519-541.
[39] 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.
[38] 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.
[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 Economic 44(2009)88-94.
[17] Lin He, Ping Hou and Zongxia Liang. Optimal control of the insurance company with proportional reinsurance policy under solvency constraintss. Insurance: Mathematics and Economic 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 26(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. Existence 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.
