PDE方法研究金融数学

信用风险评估的数学模型

信用衍生品定价

碳减排优化的数学模型

1985年郑州大学理学硕士学位

1989年北京大学理学博士学位

2000年Univ.of Edinburgh/Heriot-Watt Univ. MSc Financial Mathematics

1. Jin Liang : “The Reaction - Diffusion System without Quasi - monotone Conditions”, Acta Scientiarum Naturalium Universitatis Pekinensis, No.3 (1987) 9-20 (Chinese, English summary). Mathematics Review (M.R.).89h:35160

2. Liang Jin, ``Partial Regularity of Elliptic Systems by Blow-up method”, Bollettino U.M.I. (6) 5-A,(1986) 443-448. M.R.88a:35084

3. Liang Jin, “The Spin Wave System in Ferromagnetic Lattics”, J. Partial Differential Equations,2, No.1 (1989) 31-39.M.R.90k:82093

4. Liang Jin, “The One-Dimensional Quasilinear Verigin Problem”, J. Partial Differential Equations,4, No.2 (1991) 74-96. M.R.92f:35088

5. Jiang Lishang & Liang Jin, “The Perturbation of the Interface of the Two-dimensional Diffraction Problem and an Approximating Muskat Model”, J. Partial Differential Equations, 3, No.2 (1990) 85-96. M.R.91f:35274

6. Liang Jin, “On the Semiconductor System”, J. Partial Differential Equations,5, No. 1 (1992), 69-78. M.R.92m:35133

7. Liang Jin & Ye Qixiao, “The Monotone Method on the Sub- Strongly Coupled Reaction-Diffusion Systems”, Portugaliae Mathematica, 50, Fasc.2(1993), 193-204. M.R.94h:35120

8. J. Liang, “Weakly-Coercive Quasilinear Elliptic Equations with Inhomogeneous Measure Data” , Progress in Partial Differential Equations: Elliptic and Parabolic Problems, Pitman Research Notes in Mathematics Series266, Longman Scientific & Technical, (1992), 182-192. M.R.94b:35116

9. J. Liang, “On the Problem of Piston-like displacements in Porous Media”, Free Boundary Problems in Fluid Flow with Applications, Pitman Research Notes in Mathematics Series 282, Longman Scientific & Technical, (1993), 114-120. M.R.93k:00036

10. J. Liang, “Dirichlet Problem for a Nonlinear Integrodifferential Semiconductor System from N-Gaas Model”, Proceedings of International Conference on Differential Equations , Barcelona 1991, World Scientific, (1993),694-698.

11. J. Liang & L. Santos, “On a Kind of Nonlinear High Order Variational Inequality System”, Differential and Integral Equations,6, (1993), 1519-1530. M.R.94g:35105

12. Zhiming Chen, K.-H. Hoffmann & Jin Liang, “On a Nonstationary Ginzburg-Landau Superconductivity Model”. Mathematical Methods in the Applied Sciences16(1993), 855-875. M.R.94k:35312

13. J. Liang, “On a Nonlinear Integrodifferential Drift-Diffusion Semiconductor Model”, SIAM J. Math. Anal,25,No.5 (1994), 1375-1392. M.R.95g:35205

14. Jin Liang, “Discountinuous Nonlinearities and Free Boundary Problems”, FBP News, No.5, July (1994),4-5.

15. Jin Liang & Qin Tiehu, “Asymptotic Behaviour of Weak Solutions to Boundary Value Problem for Dynamic Viscoelastic Equation with Memory”, Proceedings of the Royal Society of Edinburgh,125A (1995), 153-164. M.R.96b:35214

16. Jin. Liang, “The Regularity of the Solution for the Curl Boundary Problems and Ginzburg-Landau Superconductivity Model”, Mathematical Models and Methods in Applied Sciences,5(1995), 529-542. M.R.96c:35155

17. Jin Liang & Tang Qi, “Asymptotic Behaviour of the Solutions of an Evolutionary Ginzburg-Landau Superconductivity Model”, J. Math. Amal. Appl.,195(1995), 92-107. M.R.96h:35209.

18. Jin Liang & J.F. Rodrigues, “Existence of Solutions for Quasilinear Weakly Coercive Elliptic Variational Inequality”, J. Partial Differential Equation,8(1995), 205-210. M.R.96h:35076.

19. A. Decarreau, Jin Liang & J. M. Rakotoson, ``Trace Imbeddings for T-Sets and Application to Neumann -Dirichlet Problems with Measures Included in the Boundary Data', Annales de la Faculte des Sciences, V (1996)443-470.

20. Jin Liang & J.F. Rodrigues, “ Quasilinear Elliptic Problems with Nonmonotone Discontinuities and Measure Data”, Portugaliae Mathematica,53(1996) 239-252. M.R.97d:35075.

21. Jin Liang, “A High Order Spin Wave System with Time Periodic Condition”, Trends in Applications of Mathematics to Mechanics, Pitman Monographs and Surveys in Pure and Applied Mathematics77, Londman (1995),37-44.

22. Jin Liang, “ Regularity of Solutions for Arbitrary Order Variational Inequalities with General Convex Sets”, Analyse Nonlineaire,14(1997),719-758.

23. Jin Liang , “On convergence of a sequence of parameterized closed convex sets and its applications”. J. Partial Differential Equations.13(2000),361-383.

24. Jin Liang, “On a High Order Spin Wave System with Nonlinear Free Term”, J. Partial Diff. Equ.19(2006)80-96.

25. Lin, Jianwei & Jin Liang “Pricing of Perpetual American and Bermudan Options by Binomial Tree Method”, Front Math. China,2(2007)243-256

26. Jin Liang, Bei Hu, Lishang Jiang & Baojun Bian, “On the Rate of Convergence of the Binomial Tree Scheme for American Options”, Numerische Mathematik107(2007)333-352

27. Jin Liang，On the Convergence Rate of the Binomial Tree Scheme for an American Option with Jump-Diffusion，Numerical Mathematics - A Journal of Chinese University，30（2008）76-96

28. 周鹏，梁进，“信用违约互换定价分析”， 高校应用数学学报22(2007), 311-314. (paper in Chinese)

29. 马俊美，梁进，“一篮子信用违约互换定价的偏微分方程方法”， 高校应用数学学报23(2008), 427-436 (paper in Chinese)

30. 吴森，梁进，高扬，“考虑经济周期的公司债券定价”，系统工程，2008 增刊（I），122-125 (paper in Chinese)

31. 高扬，梁进，“连续支付美式分期付款期权的计算”，哈尔滨工程大学学报，29（2008），1352-1355 (paper in Chinese)

32. 马俊美，纪青，李水田，梁进，“生态系统的参数确定问题”，数学的实践与认识，38（2008），105 -113. (paper in Chinese)

33. 梁进，孔亮亮，马俊美，“券商集合型基金”，同济大学学报 (2010)381550-1555 (paper in Chinese)

34. Bei Hu，Jin Liang & Lishang Jiang, , Optimal Convergence Rate of the Explicit Finite Difference Scheme for American Option Valuation, J. Comp. App. Math. 230, (2009),583-599.

35. Jin Liang, Bei Hu & Lishang Jiang， Optimal Convergence Rate of the Binomial Tree Scheme for American Options with Jump Diffusion and Their Free Boundaries, SIAM Financial Mathematics,1(2010)30-65.

36. 王涛，梁进，基于Vesicek模型的一篮子CDS定价公式解的局限性和有效性研究，系统工程 ,27(2009)No .5

37. Jin Liang, Junmei Ma, Tao Wang & Qin Ji, “Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model”, Asia-Pacific Financial Markets18(2011)33-54

38. Yujing Zhou & Jin Liang, “Valuation of a Basket Loan Credit Default Swap”, International Journal of Financial Research1(2010)21-29

39. 梁进，徐寅，郭高月，信用攸关的利率互换的定价研究， 同济大学学报 38(2010) 1550-1555 (paper in Chinese)

40. Jin Liang, Peng Zhou, Yujing Zhou & Junmei Ma, Valuation of Credit Default Swap with Counterparty Default Risk by Structural Model, Applied Mathematics2(2011)

41. 吴森，梁进，“抵押贷款信用违约互换的定价”，高校应用数学学报26, (2011) No.3,269-278.

42. Jin Liang & Yujing Zhou, Valuation of a tranched Loan Credit Default, Technology and Investment2，（2011）240-246

43. 梁进，周宇晶， “从合成担保债务契约市场报价反求期望损失的参数分析应用”，数学的实践与认识, 41 No.23, (2011)1-9

44. Sen Wu, Lishang Jiang & Jin Liang, Intensity-based Models for Pricing Mortgage-Backed Securities with Repayment Risk under a CIR Process, International Journal of Theoretical & Application Finance,15, No. 3 (2012) 12500211-17

45. Bei Hu, Lishang Jiang, Jin Liang & WeiWei, A Fully Non-linear PDE Problem from Pricing CDS with Counterparty Risk, The Journal Discrete and Continuous Dynamical System. Series B,17No.6 (2012)2001-2016

46. Jin Liang & Tao Wang, Valuation of Loan-only Credit Default Swap with Negatively Correlated Default and Prepayment Intensities, International Journal of Computer Mathematics,89,Issue 9, (2012),1255-1268

47. Yuan Wu & Jin Liang, Valuation of Loan Credit Default Swaps Correlated Prepayment and Default Risks with Stochastic Recovery Rate, International Journal of Financial Research,3, No. 2 (2012),60-68

48. 高扬，梁进，跨国公司债券的PDE定价分析，运筹与模糊学,2 No. 1, (2012)8-18

49. Jin Liang & Yang Gao, Calibration of Implied Volatility for the Exchange Rate for the Chinese Yuan from its Derivatives， Economic Modelling,29, Issue 4, (2012),1278-1285

50. Tao Wang, Jin Liang & Xiaoli Yang, Pricing for a Basket CDS and LCDS, Modern Economics, 3 No.2, ( 2012), 171-178

51. 戎嫣耘, 杨晓丽, 梁进, 结构化模型下的贷款违约互换定价, 高校应用数学学报27, (2012) No.2,146-156.

52. 梁进，王涛，杨晓丽, 考虑交易对手违约的单名LCDS定价及其CVA计算, 同济大学学报41(2013) No. 6.945-952

53. Jin Liang & Yin Xu, “Valuation of Contingent Credit Interest Rate Swap”, Risk and Decision Analysis4，No.1（2013）39-46

54. Jin Liang, Ming Yang & Lishang Jiang, A Closed-Form Solution for the Exercise Strategy in a Real Options Model with a Jump-Diffusion Process., SIAM J. of Applied Mathematics73（2013）549-571.

55. Xiaoli Yang, Jin Liang and Yuan Wu, Optimal Control of Perpetual CPDO: Minimal Cash-Out Probability and Maximal Conditional Return, to appear in Optimal Control, Applications and Methods.

56. Yin Xu， Jin Liang，Valuation of CMS-Linked TARNs， Proceeding of 13CMMSE, 2013,1428-1437

57. 杨晓丽，梁进，“一国碳减排的最小费用研究”，系统工程理论与实践接受

58. 梁进，李文毅，“含多交易对手信用违约互换风险模型”，同济大学学报，42（2014），144-150

59. 姜礼尚，梁进，“金融衍生品和信用风险定价的数学模型”，数学建模及其应用，Vol.1 (2012) 15-18

60. L.S. Jiang, & J. Liang Optimal convergence rate of the Binomial Tree Scheme for American Options and Their Free Boundaries, Frontiers in Differential. Geometry, Partial Differential Equations and Mathematical Physics, 153-167 , World Scientific. 2014

61. 梁进，曾楚琨，“基于结构化方法的含信用等级迁移的公司债券定价”，高校应用数学学报（A辑），30（2015），61-70

62. Bei Hu, Jin Liang & Yuan Wu,A Free Boundary Problem for Corporate Bondwith Credit Rating Migration, J. Math. Anal. Appl. 428 (2015) 896–909

63. 梁进，肖承志，“约化方法下具有信用等级迁移风险的零息票债券定价”，同济大学学报，43 (2015)，1284-1288 (EI）

64. Huaying Guo, Jin Liang, An optimal control model for reducing and trading of carbon emissions,Physica A: Statistical Mechanics and its Applications446,(2016), 11–21(SCI)

65. Jin Liang, Xudan Zhang, Yue juan Zhao,Utility Indifference Valuation of Corporate Bondwith Rating Migration Risk, Front. Math. China, 10(6)( 2015) 1389–1400(SCI)

66. Jin Liang,Yue juan Zhao, Xudan Z hang, ,Utility Indifference Valuation of Corporate Bond with Credit Rating Migration by Structure Approach, Economic Modelling,54,(2016),pp 339-346

67. X. Yang, J Liang & Y Wu，CPDO with Finite Termination: Maximal Return under Cash-in and Cash-out Conditions,ANZIAM Journal, 57(3),(2016),pp 207-221(SCI)

68. Huaying Guo & Jin Liang，An optimal control model of carbon reduction and trading,Mathematical Control and Related Fields, 6 (2016) 535-550(SCI)

69. Jin Liang, Yuan Wu & Bei Hu, Asymptotic Traveling Wave Solution for a Credit Rating Migration Problem,J. Differential Equations,261(2016) 1017–1045(SCI)

70. Xinfu Chen，Bei Hu, Jin Liang & Yajing Zhang, CONVERGENCE RATE OF FREE BOUNDARY OF NUMERICAL SCHEME FOR AMERICAN OPTION,Discrete and Continuous Dynamical System. Series B，21(2016) 1435-1444(SCI)

71. Xiaoli Yang & Jin Liang, Minimization of CarbonAbatement Cost: Modeling, Analysis and Simulation,Discrete and Continuous Dynamical System. Series B，22 (2017) , 2939-2970(SCI)

72. Yuan Wu, Jin Liang. A new model and its numerical method to identify multi credit migration boundaries. Accepted by International Journal of Computer Mathematics(SCI)

73. Jin Liang, , Hongming Yin, & Yuan Wu. On a Corporate Bond Pricing Model with Credit Rating Migration Risks and Stochastic Interest Rate, Quantitative Finance and Economics, 2017, 1(3): 300-319

74. 梁进，包俊利，曾楚琨，含信用等级迁移的可违约和可赎回公司债券的结构化定价，系统工程学报接受

75. Jin Liang, Ying Chen, A Free Boundary Problem for Pricing a Defaultable Restricted Callable Corporate Bonds, Proceeding of ITQM 2017

1. 数学硕士: 郑州大学数学系，导师陈国旺(1985)，论文题目：“Spin Wave System in Ferromagentic Lattics and a Nonlinear High Order Partial Differential System”；

2. 科学博士: 北京大学数学系，导师姜礼尚(1989)，论文题目：“The Perturbation of the Interface of the Diffraction Problem and the Piston-like Displacement in Porous Media”；

3. 金融数学MSC: 英国爱丁堡大学/Heriot-Watt 大学(2000)，论文题目：“ Analysis and Dynamic Programming for Measuring Brokers Performance”。

1. 《淌过博物馆》，科学普及出版社， 2012

2. 《利率互换及其衍生产品》（译）上海财经大学出版社，2013

3. 《数学建模讲义》（合）上海科学技术出版社，2014

4. 《信用风险估值的数学模型与案例分析》（合），高等教育出版社，2013

5. 《美国数学建模竞赛-同济大学优秀论文选评》（上，下，合），同济大学出版社，2014

6. 《如河的行板》，现代出版社，2015.

7. 《数学与名画》，科学出版社，2016.

8. 《淌过博物馆（第二版）》，科学普及出版社，2016.

9. 《名画中的数学密码》，科学普及出版社，2018

1. Liang, Jin; Wang, Lihe，On the occasion of the seventieth birthday of Professor Jiang Lishang. J. Partial Differential Equations 19 (2006), 1–9.

2. “用英语上专业课仍然可以有幽默”《科学时报》，2011年9月

3. “应用数学的角色”，《科学》，62 No.1 (2010) 1-2

4. “答辩博弈”，《科学新闻》，2009年12月

5. “解析次贷危机”,《科学》，61, No.2 (2009)（与姜礼尚、任学敏合作）3-8

6. “金融衍生品和信用风险定价的数学模型”, 《数学建模及其应用》 2012年6月, 15-18

7. “法国的精英是怎样炼成的” ,《上海教育.环球教育资讯》 821, No.1 (2012), 36-38

8. “走马观花看法国的精英数学教育”,《中国数学会通讯》2012 No.2

9. “郑板桥的画竹与数学建模”，《中国数学会通讯》2013 No.3

10. “工科数学”课程全英语教学的探索和实践，《同济大学双语、全英语课程建设的实践与探索》，同济出版社，2013， 183-186，（与殷俊锋 蒋凤瑛 梁进 周羚君合作）

l 一类信用衍生品的定价和优化控制研究；国家自然科学基金11271287，Study on pricing and optimal control on a kind of credit derivatives；National Science Found，主持人，2013-2016

l 信用衍生品的风险与杠杆研究，2012年度高等学校博士学科点专项科研基金课题，（Research on risks and leverage of credit derivatives，2012 University Doctor Program）主持人；2013-2015

l 评估信用等级变换风险的数学模型的理论及其应用,国家自然科学基金11671301,The theory and application on mathematical modeling for measuring credit rating migration risks,主持人，2017-2021

l 2013年国家来华留学品牌课程项目

l 2013年上海市全英语示范课程项目

l 国家级精品课程（金融衍生物定价理论，国家级）主要成员

National Excellent Course（Theory of Pricing Financial Derivatives）

l 上海市精品课程（金融衍生物定价理论，省市级）主要成员

Shanghai Excellent Course（Theory of Pricing Financial Derivatives）

l 同济大学精品课程（数学建模，校级）主要成员

Shanghai Excellent Course（Mathematical Modelling）

l 同济大学精品课程（金融衍生物定价理论，校级）主要成员

Shanghai Excellent Course（Theory of Pricing Financial Derivatives）

l 金融衍生物定价理论上海教学成果一等奖，同济大学特等奖，主要成员

First Price on TeachingAchievement（Theory of Pricing Financial Derivatives）

l 2013年国家来华留学英语授课品牌课程

2013 National Normal Course for Foreign Student (Advanced Mathematics D)

l 2013年上海市全英语示范课程

2013 Shanghai Full English Model Course (Advanced Mathematics D)

l 2009,2012年同济大学三八红旗手

l 2010，2011年教学奖励一等、二等奖

l 2009，2011年同济大学优秀指导教师奖