YAN Jia-An

Date of Birth: Dec. 6, 1941

Place of Birth: Jiangsu Province

Present Position: Member of Chinese Academy of Sciences, 

                               Professor of Academy of Mathematics and Systems Science, Chinese Academy of Sciences

E-mail Address:

Academic Experences:

  • Undergraduate student, Chinese University of Science and Technology, Beijing1959-1964

  • Assistant Professor, Institute of Mathematics , Chinese Academy of Sciences (CAS)1964-1979)

  • Associate, Professor, Institute of Applied Mathematics , CAS(1980-1986)

  • Professor, Institute of Applied Mathematics , CAS(1986-1998)

  • Professor, Academy of Mathematics and Systems Science, CAS(since 1998) 

  • Member of CAS(since 1999) 

  • Fellow,Institute of American Mathematical Statistics(since 2010)

Working Experiences:

  • 1973.3-1975.7: Visiting scholar at University of Strasbourg, France

  • 1981.1-1982.11: Humboldt fellow at Heidelberg University, Germany

  • 1986.1-1986.5: Visiting University of Strasbourg, France

  • 1992.1-1992.3: Visiting University of California at Irvine, USA

  • 1996.1-1996.3: Visiting University of Besancon, France

  • 1997.3-1997.5: Visiting Chinese University of Hong Kong, Hong Kong

  • 1998.5-1998.9; 1999.3-1999.8; 2000.8-2000.9; 2002.3-2002.4: Visiting City University of Hong Kong, Hong Kong

  • 2000.1; 2000.9: Visiting National University of Singapore, Singapore

  • 2001.7-8: Visiting Hong Kong University, Hong Kong

  • 2003.2-3,8-9; 2005.3-4; 2006.12-2007.1: Visiting Chinese University of Hong Kong, Hong Kong

  • 2005.6.15-8.15: Visiting Concordia University, Canada

  • 2006.9.1-10.28; 2007.10.1-10.25: Visiting Waterloo University, Canada

  • 2007.8.1-9.30: Visiting Illinois Institute of Technology, Iowa University, Columbia University, U.S.

  • 2008.8.1-24: Visiting Bielefeld University, Germany

  • 2008.8.25-31: Visiting University of the Witwatersrand, South Africa

  • 2009.3.1-30: Visiting Hong Kong Polytechnic University, Hong Kong

  • 2009.5.16-30: Visiting Bielefeld University, Germany

  • 2009.11.9-12.8: Visiting National University of Singapore, Singapore

  • 2010.7.1-7.30: Visiting Oxford University, UK

  • 2011.4.23-5.23: Visiting Bielefeld University, Germany

  • 2011.12.19-2012.1.9: Visiting Columbia University, U.S.

  • 2012.7.25-8.21: Visiting Delawel University, US, and Concordia University, Canada

  • 2012.9.23-9.29: Visiting ETH Zurich, Switzerland

  • 2013.6.9-7.6: Visiting Brigham Young University, and Columbia University, U.S.

  • 2015.3.9.-3.31: Visiting Princeton University, U.S.

  • 2016.1.27-2.14: Visiting Princeton University, U.S.

Professional Activities:

  • Chair of the Council of the Chines Society of Probability and Statistics(1994-1998) 

  • Member of the Committee for International Conferences of Stochastic Processes and their Applications(1992-1999) 

  • Member of the Council of the Bernoulli Society for Mathematical Statistics and Probability(1997-2001) 

  • Managing Editor of Acta Mathematica Applicatae Sinica(2002-2017) 

  • Associate Editor of Annals of Probability(2000-2002)  

  • Associate Editor of Stochastic Analysis and Applications(since 2002)

  • Associate Editor of Journal of Computational and Applied Mathematics(2003-2008)

  • Associate Editor of Insurance: Mathematics and Economics(since2008)

  • Chair of IMS-China(2008.7-2010.7)

Honors and Awards:

  • 1987 : Second-class prize for progress in sci. & tech., the Chinese Academy of Sciences

  • 1992 : First-class prize for natural sciences, the Chinese Academy of Sciences

  • 1993 : Second-class China state prize for natural sciences

  • 2006 : He-Liang-He-Li Foundation Prize for progress in sci. & tech.

  • 2007 : Hua Luo-geng Mathematical Prize

  • 2008 : Distinguished Chinese Visiting Scholar of the Hong Kong Polytechnic University

  • 2010 : IMS-Fellow

Invited Lectures at International Conferences:

  1. Some results about test and generalized functionals of white noise,

         International Conference on Probability Theory (Singapore, 1989).

  2. Constructing kernels via stochastic measures,

          International Conference on Gaussian random fields (Nagoya, 1990).

  3. From Feynman-Kac formula to Feynman integrals via analytic continuation,

          21st Conference on Stochastic Processes and their Applications (Amsterdan, 1993).

  4. Characterizations for generalized operators on distribution spaces,

          International Conference on Stochastic Calculus and Stochastic Differential Geometry (Hangzhou, China, 1995).

  5. A complex scaling approach to sequential Feynman integrals,

          24th International Conference on Stochastic Processes and their Applications (Vina Del Mar, Chile, June 16-20, 1997).

  6. A short presentation of martingale methods in option pricing,

          First Pacific Rim Conference on Mathematics (Hong Kong, Jan. 19-23, 1998).

  7. A new look at the fundamental theorem of asset pricing,

          International Conference on Probability Theory and its Applications (Taejon, Korea, Feb. 24-26, 1998).

  8. An overview on the martingale approach to option pricing,

          IMS Workshop on Applied Probability, (Chinese University of Hong Kong, Hong Kong, May 31-June 12, 1999).

  9. Some remarks on arbitrage pricing theory, 

          International Conference on Mathematical Finance, (Shanghai, China, May 10-13, 2001).

    1. Clarifying some basic concepts and results in arbitrage pricing theory,

            Quantitative methods in finance 2001 conference, (Sydney Australia, December 12-15, 2001).

    2. A Numeraire-free and Original Probability Based Framework for Financial Markets,

            International Conference on Applied Probability, (Singapore, August 16-18, 2002).

    3. A Numeraire-free and Original Probability Based Framework for Financial Markets,

            ICM 2002, (Beijing, August 20-28, 2002).

    4. Continuous-Time Mean-Risk Portfolio Selection,

            International Conference on Stochastic Processes, (in Memory of P.A. Meyer, Feb. 2-8, 2004).

    5. Markowitzs portfolio optimization in an incomplete market,

            1st Workshop on Mathematical Finance and Insurance, (Huangshan, China, May, 2004).

    6. Continuous-Time MeanCRisk Portfolio Selection,

            The Third International Congress of Chinese Mathematicians (ICCM 2004), (Hong Kong, December 17-22, 2004).

    7. An Intrinsic Characterization of No-arbitrage for Finite Discrete-Time Markets,

            Workshop on Mathematical Finance and Stochastic Analysis, (Imperial College, London, UK, August 22-24,2005).

    8. A Functional Approach to Interest Rate Modeling,

            Symposium on Stochastic Analysis and Application to Mathematical Finance, (Ritsumeikan University, Japan, March 6-10, 2006).

    9. The representations of two types of functionals on L(?,F) and L(?,F,P),

            2nd Workshop on Mathematical Finance and Insurance, (Lijiang, China, May 30-June 6, 2006).

    10. The representations of two types of functionals on L(?,F) and L(?,F,P),

            International Conference on Probability and Statistics, (Hangzhou, China, June 19 to 21, 2006).

    11. A Functional Approach to Interest Rate Modeling, 

            The 2006 international symposium on Financial Engineering and Risk Management, (Xiamen, China, July 5 to 7).

    12. An Overview of Representation Theorems for Static Risk Measures,

            International Conference on Mathematics in Finance, (Kruger National Park, South Africa, September 1-6, 2008).

    13. A new look at the Lagrange method for continuous-time stochastic optimization,

            Sino-Germany Conference on Stochastic Analysis and Related Fields, (AMSS, Beijing, May 3-7, 2010).

    14. Optimal Insurance Design under Rank Dependent Utility,

            Perspectives in Analysis and ProbabilityConference in Honor of Freddy Delbaen at ETH Zurich (September 24-28, 2012).

    15. A Note on the Monge-Kantorovich Problem in the Plane,

            Workshop on New Developments in Stochastic Analysis,Probability and PDE interactions, (AMSS, Beijing, July 8-13 , 2013).

    16. A Note on the Monge-Kantorovich Problem in the Plane,

            The First Workshop on SDEs and SPDEs, (Hefei, China, July 29th -August 1st, 2013).


    Ph-D. Students Supervised:

    • 1985-1988 Fan Ru-Zhong, Zhang Tu-Sheng

    • 1989-1992 Wu Jiang-Lun

    • 1991-1994 Wang Yong-Xiang

    • 1992-1995 Gong Fu-Zhou, Zhang Shu-Guang

    • 1993-1996 Dong Zhao, Wang Gui-Lan

    • 1994-1997 Cao Zhi-Gang, Xu Shi-Meng

    • 1996-1999 Zhang Li-Hong

    • 1997-2000 Li Ping

    • 2000-2005 Yang Haicheng, Zhou Qing

    • 2001-2006 Zhong Yucong

    • 2002-2007 Liu Xinghua, Wang Zengwu

    • 2003-2008 Huang Haitao, Qu Chang, Song Yongsheng

    • 2004-2009 Yu Baimin

    • 2006-2009 Cheng Xue

    • 2006-2011 Yao Peipei

    • 2008-2013 Deng Yulai, Shang Ke

    • 2009-2014 Ding Peizhen, Ge Yang, Sha Tao, Yue Peng

    Master Students Supervised:

    • 2005-2008 Deng Xinyu

    • 2006-2008 He Tao

    • 2007-2010 Wang Kaiwei

    • 2008-2011 You chengchao

    Research area

    Stochastic analysis
    Mathematical finance


    1. Introduction to martingales and stochastic integrals

      Shanghai Science and Tech- nology Publishing House, Shanghai, 1981.(in Chinese)

    2. Measure and Integration

      Sanxi Normal Univ. Publ. House, 1988. (in Chinese)

    3. (with He, S.W., Wang, J.G.) Semimartingale theory and stochastic calculus

      Science Press, Beijing; CRC Press, Boca Raton, FL, 1992.

    4. (with He, S.W., Wang, J.G.) Semimartingale theory and stochastic calculus

      Science Press, Beijing, 1995.(in Chinese)

    5. (with Huang, Z.Y.) Introduction to In nite Dimensional Stochastic Analysis

      Sci- ence Press, Beijing, 1997.(in Chinese)

    6. (with Peng, S.G., Fang, S.Z., Wu, L.M.) Select Topics in Stochastic Analysis

      Science Press, Beijing, 1997.(in Chinese)

    7. Introduction to Martingale Methods in Option Pricing

      LN in Math 4, Liu Bie Ju Centre for Mathematical Sciences, City Univ. of Hong Kong, 1998.

    8. Lectures on Measure Theory

      Science Press, Beijing, 1998; 2d edition, 2004; 3d edition, 2021. (in Chinese)

    9. (with Huang Z.Y.) Introduction to In nite Dimensional Stochastic Analysis

      Kluwer Academic Publishers, 2000.

    10. Introduction to Mathematical Finance

      Science Press, Beijing, 2012. (in Chinese)

    11. Introduction to Stochastic Finance

      Springer & Science Press, Beijing, 2018.


    1. Forme mesurable de la théorie des ensembles sousliniens,

      applications à la théorie de la mesure, Scientia Sinica 18 (1975), no. 4, 444-463.

    2. (with Meyer, P.A.) Génération d'une famille de tribus par un processus croissant

      Séminaire de Probabilités, IX (1975), pp. 466-470. Lecture Notes in Math., Vol. 465, Springer.

    3. (with Yoeurp, Ch.) Représentation des martingales comme intégrales stochastiques des processus optionnels

      Séminaire de Probabilités, X (1976), pp. 422-431. Lecture Notes in Math., Vol. 511, Springer.

    4. Stochastic integrals of measurable processes with respect to local martingales

      Acta Math. Sinica 21 (1978), no. 1, 18-25.(in Chinese)

    5. Remarques sur lintégrale stochastique de processus non bornés

      Séminaire de Probabilités, XIV (1980), pp. 148-151, Lecture Notes in Math., 784, Springer.

    6. Caractérisation dune classe densembles convexes de L^1 ou H^1

      ibid, 220-222.

    7. Remarques sur certaines classes de semimartingales et sur les intégrales stochastiques optionnelles

      ibid, 223-226.

    8. Sur une équation différentielle stochastique generale

      ibid, 305-315.

    9. Criteria for the uniform integrability of exponential martingales

      Acta Math. Sinica, 23 (1980), no. 2, 293-300.

    10. Some formulas for the local time of semimartingales

      Chinese Ann. Math. 1 (1980), no. 3-4, 545-551.

    11. Propriété de représentation prévisible pour les semimartingales spéciales

      Sci. Sinica, 23 (1980), no. 7, 803-813.

    12. A note on E. Lenglart's results

      Acta Math. Sinica, 23 (1980), no. 4, 638-640.

    13. Characterization of compensable processes of fi nite variation

      Chinese Ann. Math., 2 (1981), no. 4, 445-449.

    14. Uniform and L^r-integrability of exponential martingales

      Chinese Ann. Math., 3 (1982), no. 3, 285-292.

    15. A propos de lintérgrabilite uniforme des martingales exponentielles

      Séminaire de Probabilités, XVI (1982), 338-347. Lecture Notes in Math., Vol. 920, Springer.


    1. Martingales Locales sur un Ouvert Droit Optionnel

      Stochastics 8 (1982/83), no. 3, 161-180.

    2. Une remarque sur les solutions faibles des équations différentielles stochastiques unidimensionnelles

      Seminaire de Probabilites, XVII (1983), 78-80. Lecture Notes in Math., Vol. 986, Springer.

    3. Sur un theoreme de Kazamaki-Sekiguchi

      ibid, 121-122.

    4. (with He, S.W., Zheng, W.A.) Sur la convergence des semimartingales continues dans R^n et des martingales dans une variété

      ibid, 179-184.

    5. (with Emery, M., Stricker, C.) Valeurs Prises par les Martingales Locales Continues à un Instant Donne

      Ann. Probab., 11 (1983), no. 3, 635-641.

    6. On the extensions of measures

      Dongbei-Shida-Xuebao [Journal of Northeast Nor- mal University, Natural Sciences] 1984, no. 1, 1-11. (in Chinese)

    7. A formula for local times of semimartingales

      Dongbei-Shuxue [Northeastern- Mathematical- Journal] 1 (1985), no. 2, 138-140.

    8. A simple proof of El Karouis upcrossing theorem for semimartingales

      Journal of Mathematical Research and Exposition, 5 (1985), no. 2, 127-129.

    9. On the commutability of essential infimum and conditional expectation operations

      Kexue-Tongbao (Science Bulletin), 30 (1985), no. 8, 1013-1018.

    10. A comparison theorem for semimartingales and its applications

      Seminaire de Probabilit es, XX (1986), 349-351, Lecture Notes in Math., 1204, Springer.

    11. (with Meyer, P.A.) A propos des distributions sur lespace de Wiener

      Séminaire de Probabilités, XXI (1987), 8-26, Lecture Notes in Math., 1247, Springer.

    12. Developpement des distributions suivant les chaos de Wiener et applications à l'analyse stochastique

      ibid, 27-32.

    13. A perturbation theorem for semigroups of linear operators

      Séminaire de Probabilités, XXII (1988), 89-91, Lecture Notes in Math., 1321, Springer.

    14. A formula for densities of transition functions

      ibid, 92-100.

    15. On the existence of diffusions with singular drift coefficient

      Acta Math. Appl. Sinica (English Ser.), 4 (1988), no. 1, 23-29.


    1. A change of variables formula for local times of semimartingales

      Kexue-Tongbao (Science Bulletin), 33 (1988), 1755-1759.

    2. (with Meyer, P.A..) Distributions sur l'espace de Wiener (suite),

      daprès I. Kubo et Y. Yokoi, Séminaire de Probabilités, XXIII (1989), 382-392, Lecture Notes in Math., 1372, Springer.

    3. Sur la transformée de Fourier de H. H. Kuo

      ibid, 393-394.

    4. Generalizations of Gross and Minlos theorems

      ibid, 395-404.

    5. On the existence of density of the law of a Wiener functional

      Acta Math. Sinica, New-Series, 5 (1989), no. 2, 97-100.

    6. On monotone class theorems

      Dongbei-Shuxue [Northeastern Mathematical Jour- nal] 5 (1989), no. 1, 59-66. (in Chinese)

    7. (with Zhang, T.S.) Dirichlet forms and symmetric di usions on a bounded domain in Rd

      Chinese Ann. Math. Ser. A 11 (1990), no. 5, 667-674.

    8. (with Zhang, T.S.) Dirichlet forms and potential theory of symmetric Hunt processes

      Science in China (Scientia Sinica), Series-A. 33 (1990), no. 7, 800-809.

    9. A remark on conditional expectations

      Chinese Sci. Bull., 35 (1990), no. 9, 719-722.

    10. A review of studies in probability theory and stochastic analysis

      Probability theory and its applications in China, 313-327, Contemp. Math., 118, Amer. Math. Soc., Providence, RI, 1991.

    11. (with Meyer, P.A.) Les fonctions caractéristiques des distributions sur l'espace de Wiener

      Séminaire de Probabilités, XXV (1991), 61-78, Lecture Notes in Math., 1485, Springer.

    12. Notes on the Wiener semigroup and renormalization

      ibid, 79-94.

    13. Some remarks on the theory of stochastic integration

      ibid, 95-107.

    14. Constructing kernels via stochastic measures

      Gaussian random elds (Nagoya, 1990), 396-405, Ser. Probab. Statist., 1, World Sci. Publishing, River Edge, NJ, 1991.

    15. An elementary proof of a theorem of Lee

      Acta Math. Sci. (English Ed.) 11 (1991), no. 3, 356-360.


    1. (with Kuo, H.-H., Potthoff, J.) Continuity of affine transformations of white noise test functionals and applications

      Stochastic Process. Appl., 43 (1992), no. 1, 85-98.

    2. (with Potthoff, J.) Some results about test and generalized functionals of white noise

      In: Probability theory, eds- L.Y. Chen et al., Walter de Gruyter, Berlin, 1992, 121-145.

    3. A formula for continuous additive functionals of nonsymmetric Hunt processes and application to Feynman-Kac transition functions

      Probability and statistics (Tian- jin, 1988/1989), 228-241, Nankai Ser. Pure Appl. Math. Theoret. Phys., World Sci. Publishing, River Edge, NJ, 1992.

    4. Inequalities for products of white noise functionals

      In: Stochastic processes, Springer, New York, 1993.

    5. Some recent developments in wite nois analysis

      In: Probability and Statistics, eds- Badrikian et al., World Scienti%0Cc, 1993, 221-248.

    6. Notes on Lévy Laplacian operator

      Chinese Sci. Bull., 39 (1994), 6-11.

    7. (with Liu, K.) Euler operator and homogeneous Hida distributions

      Acta Math. Sinica (N.S.), 10 (1994), no. 4, 439-445.

    8. From Feynman-Kac formula to Feynman integrals via analytic continuation

      Stochastic Process. Appl., 54 (1994), no. 2, 215-232.

    9. (with Carmona, R.A.) A new space of white noise distributions and applications to SPDEs

      Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1993), 51-66, Progr. Probab., 36, Birkhauser, Basel, 1995.

    10. Products and transforms of white-noise functionals (in general setting)

      Appl. Math. Optim., 31 (1995), no. 2, 137-153.

    11. (with Imkeller, P.) Multiple intersection local time of planar Brownian motion as a particular Hida distribution

      J. Funct. Anal., 140 (1996), no. 1, 256-273.

    12. (with Imkeller, P.) New distributions over Wiener and Euclidean spaces

      Science in China, Ser. A. 39 (1996), 925-934.

    13. An asymptotic evaluation of heat kernel for short time

      Sem. Probab. XXX (1996), LN. in Math. 1626, Springer, 104-107.

    14. A new look at the fundamental theorem of asset pricing

      J. Korean Math. Soc. Vol. 35, No. 3 (1998), 659-673.

    15. (with Kondratiev, Y.G., Streit, L.,Westerkamp, W.) Generalized functions in in nite dimensional analysis

      Hiroshima Mathematical Journal, 28(1998), 213-260.


    1. (with C. Stricker) Some remarks on the optional decomposition theorem

      Séminaire de Probab. XXXII (1998), LN in Math. 1686, Springer, 56-66.

    2. (with S. L. Luo) Characterization of continuous operators on in nite dimensional distribution spaces

      In: Proceedings of Second International Workshop, Stoch. Anal. and Math. Physics, Edited by R. Rebolledo, World Scienti c, 1998, 120-134.

    3. (with S. L. Luo) On Wick product of general operators

      Chinese Science Bulltin, Vol. 43, No. 15, 1252-1256.

    4. (with S. L. Luo) Generalized Fourier- Mehler transforms on white noise functional spaces

      Chinese Science Bulletin, Vol. 43, No. 16, 1321-1325.

    5. (with S. L. Luo) A complex scaling approach to sequential Feynman integrals

      Stoch. Processes and their Appl. 79 (1999), 287-300.

    6. (with Cao, Z.) A comparison theorem for solutions of backward stochstic di erential equations

      Advance in Mathematics, Vol. 28, No.1 (1999), 304-308.

    7. (with Luo, S.L.) Gaussian kernel operators on white noise functional spaces

      Science in China, 43(10), 2000, 1067-1074.

    8. (with Zhang Q. and Zhang, S.G.) Growth optimal portfolio in a market driven by a jump-diffusion-like process or a Lévy process

      Annals of Economics and Finance, 1(1), 2000, 101-116.

    9. (with Li P. and Xia, J.M.) Martingale measure method for expected utility maximization in discrete time incomplete markets

      Annals of Economics and Finance, 2(2), 2001, 445-465.

    10. (with Li, P.) The growth optimal portfolio in discrete-time nancial markets

      Advances in Mathematics, 2002, Vol.31, No.6, 537-542.

    11. (with Xia, J.M.) Some remarks on arbitrage pricing theory

      In: Recent Developments in Mathematical Finance, World Scienti%0Cc, 2002, 218-227.

    12. (with Luo, S.L. and Zhang, Q.) Arbitrage pricing systems in a market driven by an It? process

      In: Recent Developments in Mathematical Finance, World Sci. Publ., River Edge, NJ, 2002, 263-271.

    13. (with Tang, Q.H.)A sharp inequality for the tail probabilities of sums of i.i.d. r.v.s with dominatedly varying tails

      Science in China (Series A), 45(8), 2002, 1006-1011.

    14. An overview on the martingale approach to option pricing

      AWS/IP Studies in Advanced Mathematics, Volume 26, 2002, 121-134.

    15. A numeraire-free and original probability based framework for nancial markets

      Proceedings of the ICM 2002, Vol. III, 861-871.


    1. (with Liu, W. and Yang, W. G.) A limit theorem for partial sums of random variables and its applications

      Statistics and Probability Letters, 62(1), 2003, 79-86.

    2. (with Ng, K., Tang, Q. and Yang, H.) Precise large deviations for the prospective- loss process

      J. Appl. Prob. 40, 2003, 391-400.

    3. (with Xia, J.M.) A new look at basic concepts in arbitrage pricing theory

      Science in China (Series A), 46(6), 2003, 764-774.

    4. (with Ng, K., Tang, Q. and Yang, H.) Precise large deviations for sums of random variables with consistently varying tails

      J. Appl. Prob. 41, 2004, 93-107.

    5. (with Jin, H. and Zhou, X.Y.) Continuous-Time Mean-Risk Portfolio Selection

      Ann. I. H. Poincar - PR 41, 2005, 559-580.

    6. (with Xia, J.M.) Markowitzs portfolio optimization in an incomplete market

      Mathematical Finance, Vol. 16, No. 1, 2006, 203-216.

    7. A simple proof of two generalized Borel-Cantelli lemmas

      Seminaire de Probabilites, XXV (2006), 77-79, Lecture Notes in Math., 1874, Springer.

    8. (with Song, Y.)The representations of two types of functionals on L(\Omega ,F) and L(\Omega ,F, P)

      Science in China Series A-Mathematics 2006 Vol.49, No. 10 pp.1376- 1382.

    9. (with Wang, Z.W.) A selective overview of applications of Choquet integrals

      Advanced Lectures in Mathematics, Higher Educational Press and International Press, 2007, 484-514.

    10. (with Xia, J.) Convex Duality for Optimal Investment

      AMS/IP Studies in Ad- vanced Mathematics, 2008, Volume 42, 663-678.

    11. (with Duan, J.) General matrix-valued inhomogeneous linear stochastic differential equations and applications

      Statistics and Probability Letters 78 (2008) 2361-2365.

    12. (with Zhou, X.)Markovitz Strategies Revised

      Acta Mathematica Scientia 2009,29B(4), 817-828.

    13. (with Song, Y.) An overview of representation theorems for static risk measures

      Science in China Series A: Mathematics, 2009, Vol. 52, Issue 7, 1412 - 1422

    14. (with Hu, Y.) Wick calculus for nonlinear Gaussian functionals

      Acta Mathematica Applicatae Sinica, English Series, Vol. 25, No.3 (2009), 399-414.

    15. (with Song, Y.) Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders

      In: Mathematics and Economics, 2009, Vol. 45, 459- 465.


    1. A short presentation of Choquet integral, in Recent Development in Stochastic Dynamics and Stochastic Analysis

      Interdisciplinary Mathematical Science, Vol.8, 2010, Eds: J. Duan et. al., Wold Scienti c, 269-291.

    2. (with S. L. Luo and Q. Zhang) A functional transformation approach to interest rate modeling

      in Stochastic Processes, Finance and Control, edited by Cohen et al., World Scienti c, pp. 303-316, 2012.

    3. (with X. Cheng) A new look at the Lagrange method for continuous-time stochastic optimization

      Science China Mathematics, Vol. 55 No. 11: 2247-2258, 2012.

    4. (with X. Cui, D. Li)Classical mean-variance model revisited: pseudo eciency

      Journal of the Operational Research Society (2015) 66, 1646-1655.

    5. (with Z. Xu)A note on the Monge-Kantorovich problem in the plane

      Communication on pure and applied analysis, 2015, 14(2), 517-525.

    6. (with C. Bernard, X.D. He, and X.Y. Zhou)Optimal insurance design under rank-dependent expected utility

      Mathematical Finance, 2015, 25(1), 154-186.


    (Address) Academy of Mathematics and Systems Science, CAS , No.55, Zhong-guan-cun East Road Beijing 100190, China