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Volumn , Issue , 2007, Pages 541-567

G-Expectation, G-brownian motion and related stochastic calculus of itô type

Author keywords

Brownian motion; BSDE; G expectation; G normal distribution; Gaussian process; It 's formula; It 's integral; It 's stochastic calculus; Nonlinear expectation; Nonlinear probability theory; Quadratic variation process; SDE

Indexed keywords

BROWNIAN MOVEMENT; CALCULATIONS; DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS; NORMAL DISTRIBUTION;

EID: 84883606894     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-70847-6_25     Document Type: Conference Paper
Times cited : (653)

References (45)
  • 3
    • 84953009457 scopus 로고
    • Pricing and hedging derivative securities in markets with uncertain volatilities
    • Avellaneda, M., Levy, A. and Paras, A. (1995). Pricing and hedging derivative securities in markets with uncertain volatilities. Appl. Math. Finance 2, 73-88.
    • (1995) Appl. Math. Finance , vol.2 , pp. 73-88
    • Avellaneda, M.1    Levy, A.2    Paras, A.3
  • 4
    • 0001503403 scopus 로고    scopus 로고
    • A converse comparison theorem for BSDEs and related properties of g-expectations
    • Briand, Ph., Coquet, F., Hu, Y., Mémin J. and Peng, S. (2000) A converse comparison theorem for BSDEs and related properties of g-expectations, Electron. Comm. Probab, 5.
    • (2000) Electron. Comm. Probab , vol.5
    • Briand, Ph.1    Coquet, F.2    Hu, Y.3    Mémin, J.4    Peng, S.5
  • 5
    • 0013296544 scopus 로고    scopus 로고
    • A property of backward stochastic differential equations
    • Chen, Z. (1998) A property of backward stochastic differential equations, C. R. Acad. Sci. Paris Sér. I Math. 326(4), 483-488.
    • (1998) C. R. Acad. Sci. Paris Sér. i Math. , vol.326 , Issue.4 , pp. 483-488
    • Chen, Z.1
  • 6
    • 0036077604 scopus 로고    scopus 로고
    • Ambiguity, risk and asset returns in continuous time
    • Chen, Z. and Epstein, L. (2002), Ambiguity, Risk and Asset Returns in Continuous Time, Econometrica, 70(4), 1403-1443.
    • (2002) Econometrica , vol.70 , Issue.4 , pp. 1403-1443
    • Chen, Z.1    Epstein, L.2
  • 8
    • 84863229852 scopus 로고    scopus 로고
    • A nonlinear doob-meyer type decomposition and its application
    • (Japan)
    • Chen, Z. and Peng, S. (1998) A Nonlinear Doob-Meyer type Decomposition and its Application. SUT Journal of Mathematics (Japan), 34(2), 197-208.
    • (1998) SUT Journal of Mathematics , vol.34 , Issue.2 , pp. 197-208
    • Chen, Z.1    Peng, S.2
  • 9
    • 0013198407 scopus 로고    scopus 로고
    • A general downcrossing inequality for g-martingales
    • Chen, Z. and Peng, S. (2000), A general downcrossing inequality for g-martingales, Statist. Probab. Lett. 46(2), 169-175.
    • (2000) Statist. Probab. Lett. , vol.46 , Issue.2 , pp. 169-175
    • Chen, Z.1    Peng, S.2
  • 11
    • 0042238470 scopus 로고    scopus 로고
    • A general converse comparison theorem for backward stochastic differential equations
    • Serie I
    • Coquet, F., Hu, Y., Mémin, J. and Peng, S. (2001) A general converse comparison theorem for Backward stochastic differential equations, C. R. Acad. Sci. Paris, t.333, Serie I, 577-581.
    • (2001) C. R. Acad. Sci. Paris , vol.333 , pp. 577-581
    • Coquet, F.1    Hu, Y.2    Mémin, J.3    Peng, S.4
  • 12
    • 0036016204 scopus 로고    scopus 로고
    • Filtration-consistent nonlinear expectations and related g-expectations
    • Coquet, F., Hu, Y., Memin J. and Peng, S. (2002), Filtration-consistent nonlinear expectations and related g-expectations, Probab. Theory Relat. Fields, 123, 1-27.
    • (2002) Probab. Theory Relat. Fields , vol.123 , pp. 1-27
    • Coquet, F.1    Hu, Y.2    Memin, J.3    Peng, S.4
  • 13
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall, M., Ishii, H., and Lions, P.-L. (1992) User's Guide To Viscosity Solutions Of Second Order Partial Differential Equations, Bulletin Of The American Mathematical Society, 27(1), 1-67.
    • (1992) Bulletin of the American Mathematical Society , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.-L.3
  • 14
    • 3943062117 scopus 로고
    • A general form of integral
    • Daniell, P.J. (1918) A general form of integral. Annals of Mathematics, 19, 279-294.
    • (1918) Annals of Mathematics , vol.19 , pp. 279-294
    • Daniell, P.J.1
  • 15
    • 0003856407 scopus 로고    scopus 로고
    • (Lectures given at the Cattedra Galileiana at the Scuola Normale di Pisa, March 2000), Published by the Scuola Normale di Pisa
    • Delbaen, F. (2002), Coherent Risk Measures (Lectures given at the Cattedra Galileiana at the Scuola Normale di Pisa, March 2000), Published by the Scuola Normale di Pisa.
    • (2002) Coherent Risk Measures
    • Delbaen, F.1
  • 16
    • 84883612716 scopus 로고    scopus 로고
    • Pricing, hedging and optimally designing derivatives via minimization of risk measures
    • Preprint, to appear
    • Barrieu, P. and El Karoui, N. (2004) Pricing, Hedging and Optimally Designing Derivatives via Minimization of Risk Measures, Preprint, to appear in Contemporary Mathematics.
    • (2004) Contemporary Mathematics
    • Barrieu, P.1    El Karoui, N.2
  • 18
    • 0002335001 scopus 로고
    • Dynamic programming and pricing of contingent claims in incomplete market
    • El Karoui, N., Quenez, M.C. (1995) Dynamic Programming and Pricing of Contingent Claims in Incomplete Market. SIAM J. of Control and Optimization, 33(1).
    • (1995) SIAM J. of Control and Optimization , vol.33 , Issue.1
    • El Karoui, N.1    Quenez, M.C.2
  • 19
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic differential equation in finance
    • El Karoui, N., Peng, S., Quenez, M.C. (1997) Backward stochastic differential equation in finance, Mathematical Finance 7(1): 1-71.
    • (1997) Mathematical Finance , vol.7 , Issue.1 , pp. 1-71
    • El Karoui, N.1    Peng, S.2    Quenez, M.C.3
  • 22
    • 84886480444 scopus 로고
    • Differential equations determining a markoff process
    • Kiyosi Itô Edit. D.W. Strook and S.R.S. Varadhan, Springer Translated from the original Japanese first published in Japan, Pan-Japan Math. Coll. No. 1077
    • Itô, Kiyosi, (1942) Differential Equations Determining a Markoff Process, in Kiyosi Itô: Selected Papers, Edit. D.W. Strook and S.R.S. Varadhan, Springer, 1987, Translated from the original Japanese first published in Japan, Pan-Japan Math. Coll. No. 1077.
    • (1942) Selected Papers
    • Itô, K.1
  • 23
    • 1642323877 scopus 로고    scopus 로고
    • Some results on the uniqueness of generators of backward stochastic differential equations
    • Ser. I
    • Jiang, L. (2004) Some results on the uniqueness of generators of backward stochastic differential equations, C. R. Acad. Sci. Paris, Ser. I 338 575-580.
    • (2004) C. R. Acad. Sci. Paris , vol.338 , pp. 575-580
    • Jiang, L.1
  • 24
    • 42249105380 scopus 로고    scopus 로고
    • A result on the probability measures dominated by g-expectation
    • English Series
    • Jiang L. and Chen, Z. (2004) A result on the probability measures dominated by g-expectation, Acta Mathematicae Applicatae Sinica, English Series 20(3) 507-512.
    • (2004) Acta Mathematicae Applicatae Sinica , vol.20 , Issue.3 , pp. 507-512
    • Jiang, L.1    Chen, Z.2
  • 27
    • 84963386901 scopus 로고
    • Uncertain volatility and the risk free synthesis of derivatives
    • Lyons, T. (1995). Uncertain volatility and the risk free synthesis of derivatives. Applied Mathematical Finance 2, 117-133.
    • (1995) Applied Mathematical Finance , vol.2 , pp. 117-133
    • Lyons, T.1
  • 28
    • 84967782855 scopus 로고
    • On a nonlinear semigroup attached to optimal stochastic control
    • Nisio, M. (1976) On a nonlinear semigroup attached to optimal stochastic control. Publ. RIMS, Kyoto Univ., 13: 513-537.
    • (1976) Publ. RIMS, Kyoto Univ. , vol.13 , pp. 513-537
    • Nisio, M.1
  • 29
    • 20744436463 scopus 로고
    • On stochastic optimal controls and envelope of Markovian semi-groups
    • Nisio, M. (1976) On stochastic optimal controls and envelope of Markovian semi-groups. Proc. of int. Symp. Kyoto, 297-325.
    • (1976) Proc. of Int. Symp. Kyoto , pp. 297-325
    • Nisio, M.1
  • 31
    • 0025262967 scopus 로고
    • Adapted solution of a backward stochastic differential equation
    • Pardoux, E., Peng, S. (1990) Adapted solution of a backward stochastic differential equation. Systems and Control Letters, 14(1): 55-61.
    • (1990) Systems and Control Letters , vol.14 , Issue.1 , pp. 55-61
    • Pardoux, E.1    Peng, S.2
  • 32
    • 0001098095 scopus 로고
    • A generalized dynamic programming principle and hamilton-jacobi-bellman equation
    • Peng, S. (1992) A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation. Stochastics and Stochastic Reports, 38(2): 119-134.
    • (1992) Stochastics and Stochastic Reports , vol.38 , Issue.2 , pp. 119-134
    • Peng, S.1
  • 33
    • 0000093726 scopus 로고    scopus 로고
    • Backward SDE and related g-expectation
    • Pitman Research Notes in Math. Series, No. 364, El Karoui Mazliak edit
    • Peng, S. (1997) Backward SDE and related g-expectation, in Backward Stochastic Differential Equations, Pitman Research Notes in Math. Series, No. 364, El Karoui Mazliak edit. 141-159.
    • (1997) Backward Stochastic Differential Equations , pp. 141-159
    • Peng, S.1
  • 34
    • 20744450906 scopus 로고    scopus 로고
    • BSDE and stochastic optimizations
    • Yan, J., Peng, S., Fang, S., Wu, L.M. Ch.2, (Chinese vers.), Science Publication, Beijing
    • Peng, S. (1997) BSDE and Stochastic Optimizations, Topics in Stochastic Analysis, Yan, J., Peng, S., Fang, S., Wu, L.M. Ch.2, (Chinese vers.), Science Publication, Beijing.
    • (1997) Topics in Stochastic Analysis
    • Peng, S.1
  • 35
    • 0039529012 scopus 로고    scopus 로고
    • Monotonic limit theorem of BSDE and nonlinear decomposition theorem of doob-meyer's type
    • Peng, P. (1999) Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type, Prob. Theory Rel. Fields 113(4) 473-499.
    • (1999) Prob. Theory Rel. Fields , vol.113 , Issue.4 , pp. 473-499
    • Peng, P.1
  • 36
    • 24144442604 scopus 로고    scopus 로고
    • Nonlinear expectation, nonlinear evaluations and risk measures
    • K. Back, T.R. Bielecki, C. Hipp, S. Peng, W. Schachermayer C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy (Edit. M. Frittelli and W. Runggaldier) LNM 1856, Springer-Verlag
    • Peng, S. (2004) Nonlinear expectation, nonlinear evaluations and risk measures, in K. Back, T.R. Bielecki, C. Hipp, S. Peng, W. Schachermayer, Stochastic Methods in Finance Lectures, C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy 2003, (Edit. M. Frittelli and W. Runggaldier) 143-217, LNM 1856, Springer-Verlag.
    • (2003) Stochastic Methods in Finance Lectures , pp. 143-217
    • Peng, S.1
  • 37
    • 7244231371 scopus 로고    scopus 로고
    • Filtration consistent nonlinear expectations and evaluations of contingent claims
    • English Series
    • Peng, S. (2004) Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, English Series 20(2), 1-24.
    • (2004) Acta Mathematicae Applicatae Sinica , vol.20 , Issue.2 , pp. 1-24
    • Peng, S.1
  • 38
    • 20744446139 scopus 로고    scopus 로고
    • Nonlinear expectations and nonlinear Markov chains
    • Peng, S. (2005) Nonlinear expectations and nonlinear Markov chains, Chin. Ann. Math. 26B(2), 159-184.
    • (2005) Chin. Ann. Math. , vol.26 B , Issue.2 , pp. 159-184
    • Peng, S.1
  • 39
    • 7244227897 scopus 로고    scopus 로고
    • Dynamical evaluations
    • Ser. I
    • Peng, S. (2004) Dynamical evaluations, C. R. Acad. Sci. Paris, Ser. I 339 585-589.
    • (2004) C. R. Acad. Sci. Paris , vol.339 , pp. 585-589
    • Peng, S.1
  • 44
    • 84883619020 scopus 로고    scopus 로고
    • Some examples of risk measures via g-expectations
    • preprint, to appear
    • Rosazza Giannin, E., (2002) Some examples of risk measures via g-expectations, preprint, to appear in Insurance: Mathematics and Economics.
    • (2002) Insurance: Mathematics and Economics
    • Rosazza Giannin, E.1


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