메뉴 건너뛰기




Volumn 43, Issue 5, 2005, Pages 1676-1713

Sensitivity analysis using Itô-malliavin calculus and martingales, and application to stochastic optimal control

Author keywords

Malliavin calculus; Parameterized control; Sensitivity analysis; Weak approximation

Indexed keywords

COSTS; FINANCE; FUNCTIONS; PARAMETER ESTIMATION; PROBLEM SOLVING; SENSITIVITY ANALYSIS; STOCHASTIC CONTROL SYSTEMS;

EID: 27644539475     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012902419059     Document Type: Article
Times cited : (96)

References (52)
  • 1
    • 3042803039 scopus 로고    scopus 로고
    • Stability of stochastic differential equations in manifolds
    • [AT98], Springer-Verlag, Berlin
    • [AT98] M. ARNAUDON AND A. THALMAIER, Stability of stochastic differential equations in manifolds, in Séminaire de Probabilités, XXXII, Springer-Verlag, Berlin, 1998, pp. 188-214.
    • (1998) Séminaire de Probabilités , vol.32 , pp. 188-214
    • Arnaudon, M.1    Thalmaier, A.2
  • 2
    • 0013535965 scopus 로고    scopus 로고
    • Infinite-horizon gradient-based policy search
    • [BB01]
    • [BB01] J. BAXTER AND P.L. BARTLETT, Infinite-horizon gradient-based policy search, J. Artificial Intelligence Res., 15 (2001), pp. 319-350.
    • (2001) J. Artificial Intelligence Res. , vol.15 , pp. 319-350
    • Baxter, J.1    Bartlett, P.L.2
  • 4
    • 0001064964 scopus 로고    scopus 로고
    • Estimating security price derivatives using simulation
    • [BG96]
    • [BG96] M. BROADIE AND P. GLASSERMAN, Estimating security price derivatives using simulation, Management Sci., 42 (1996), pp. 269-285.
    • (1996) Management Sci. , vol.42 , pp. 269-285
    • Broadie, M.1    Glasserman, P.2
  • 7
    • 0030560429 scopus 로고    scopus 로고
    • The law of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function
    • [BT96a]
    • [BT96a] V. BALLY AND D. TALAY, The law of the Euler scheme for stochastic differential equations: I. Convergence rate of the distribution function, Probab. Theory Related Fields, 104 (1996), pp. 43-60.
    • (1996) Probab. Theory Related Fields , vol.104 , pp. 43-60
    • Bally, V.1    Talay, D.2
  • 9
    • 0010626275 scopus 로고    scopus 로고
    • On dynamic measures of risk
    • [CK99]
    • [CK99] J. CVITANIĆ AND I. KARATZAS, On dynamic measures of risk, Finance Stoch., 3 (1999), pp. 451-482.
    • (1999) Finance Stoch. , vol.3 , pp. 451-482
    • Cvitanić, J.1    Karatzas, I.2
  • 10
    • 0036025135 scopus 로고    scopus 로고
    • Hypoelliptic non-homogeneous diffusions
    • [CM02]
    • [CM02] P. CATTIAUX AND L. MESNAGER, Hypoelliptic non-homogeneous diffusions, Probab. Theory Related Fields, 123 (2002), pp. 453-483.
    • (2002) Probab. Theory Related Fields , vol.123 , pp. 453-483
    • Cattiaux, P.1    Mesnager, L.2
  • 11
    • 0034825435 scopus 로고    scopus 로고
    • Stochastic linear quadratic optimal control problems
    • [CY01]
    • [CY01] S. CHEN AND J. YONG, Stochastic linear quadratic optimal control problems, Appl. Math. Optim., 43 (2001), pp. 21-45.
    • (2001) Appl. Math. Optim. , vol.43 , pp. 21-45
    • Chen, S.1    Yong, J.2
  • 13
  • 15
    • 0022882413 scopus 로고
    • Stochastic approximation for Monte Carlo optimization
    • [Gly86], J. Wilson, J. Henriksen, and S. Roberts, eds.
    • [Gly86] P. W. GLYNN, Stochastic approximation for Monte Carlo optimization, in Proceedings of the 1986 Winter Simulation Conference, J. Wilson, J. Henriksen, and S. Roberts, eds., 1986, pp. 356-365.
    • (1986) Proceedings of the 1986 Winter Simulation Conference , pp. 356-365
    • Glynn, P.W.1
  • 16
    • 0023543886 scopus 로고
    • Likelihood ratio gradient estimation: An overview
    • [Gly87], A. Thesen, H. Grant, and W. D. Kelton, eds.
    • [Gly87] P. W. GLYNN, Likelihood ratio gradient estimation: An overview, in Proceedings of the 1987 Winter Simulation Conference, A. Thesen, H. Grant, and W. D. Kelton, eds., 1987, pp. 366-375.
    • (1987) Proceedings of the 1987 Winter Simulation Conference , pp. 366-375
    • Glynn, P.W.1
  • 17
    • 27644519070 scopus 로고    scopus 로고
    • Sensitivity analysis using Itô-Malliavin calculus and martingales. Numerical implementation
    • [GM03], CMAP, Ecole Polytechnique, Palaiseau, France
    • [GM03] E. GOBET AND R. MUNOS, Sensitivity Analysis using Itô-Malliavin Calculus and Martingales. Numerical Implementation, Technical report 520, CMAP, Ecole Polytechnique, Palaiseau, France, 2003.
    • (2003) Technical Report , vol.520
    • Gobet, E.1    Munos, R.2
  • 18
    • 0012074125 scopus 로고    scopus 로고
    • Euler schemes for the weak approximation of killed diffusion
    • [Gob00]
    • [Gob00] E. GOBET, Euler schemes for the weak approximation of killed diffusion, Stochastic Process. Appl., 87 (2000), pp. 167-197.
    • (2000) Stochastic Process. Appl. , vol.87 , pp. 167-197
    • Gobet, E.1
  • 19
    • 84996131097 scopus 로고    scopus 로고
    • Euler schemes and half-space approximation for the simulation of diffusions in a domain
    • [Gob01a]
    • [Gob01a] E. GOBET, Euler schemes and half-space approximation for the simulation of diffusions in a domain, ESAIM Probab. Statist., 5 (2001), pp. 261-297.
    • (2001) ESAIM Probab. Statist. , vol.5 , pp. 261-297
    • Gobet, E.1
  • 20
    • 0009936666 scopus 로고    scopus 로고
    • Local asymptotic mixed normality property for elliptic diffusion: A Malliavin calculus approach
    • [Gob01b]
    • [Gob01b] E. GOBET, Local asymptotic mixed normality property for elliptic diffusion: A Malliavin calculus approach, Bernoulli, 7 (2001), pp. 899-912.
    • (2001) Bernoulli , vol.7 , pp. 899-912
    • Gobet, E.1
  • 21
    • 0036334160 scopus 로고    scopus 로고
    • LAN property for ergodic diffusion with discrete observations
    • [Gob02]
    • [Gob02] E. GOBET, LAN property for ergodic diffusion with discrete observations, Ann. Inst. H. Poincaré Probab. Statist., 38 (2002), pp. 711-737.
    • (2002) Ann. Inst. H. Poincaré Probab. Statist. , vol.38 , pp. 711-737
    • Gobet, E.1
  • 23
    • 0000728309 scopus 로고
    • Some guidelines and guarantees for common random numbers
    • [GY92]
    • [GY92] P. GLASSERMAN AND D. D. YAO, Some guidelines and guarantees for common random numbers, Management Sci., 38 (1992), pp. 884-908.
    • (1992) Management Sci. , vol.38 , pp. 884-908
    • Glasserman, P.1    Yao, D.D.2
  • 25
    • 22044434402 scopus 로고    scopus 로고
    • Asymptotic error distributions for the Euler method for stochastic differential equations
    • [JP98]
    • [JP98] J. JACOD AND P. PROTTER, Asymptotic error distributions for the Euler method for stochastic differential equations, Ann. Probab., 26 (1998), pp. 267-307.
    • (1998) Ann. Probab. , vol.26 , pp. 267-307
    • Jacod, J.1    Protter, P.2
  • 26
    • 0343893613 scopus 로고    scopus 로고
    • Actor-critic-type learning algorithms for Markov decision processes
    • [KB99]
    • [KB99] V. R. KONDA AND V. S. BORKAR, Actor-critic-type learning algorithms for Markov decision processes, SIAM J. Control Optim., 38 (1999), pp. 94-123.
    • (1999) SIAM J. Control Optim. , vol.38 , pp. 94-123
    • Konda, V.R.1    Borkar, V.S.2
  • 27
    • 0003924011 scopus 로고    scopus 로고
    • Numerical methods for stochastic control problems in continuous time, 2nd ed
    • [KD01], Springer-Verlag, New York
    • [KD01] H. J. KUSHNER AND P. DUPUIS, Numerical Methods for Stochastic Control Problems in Continuous Time, 2nd ed., Appl. Math. 24, Springer-Verlag, New York, 2001.
    • (2001) Appl. Math. , vol.24
    • Kushner, H.J.1    Dupuis, P.2
  • 28
    • 0035625675 scopus 로고    scopus 로고
    • Weak approximations. A Malliavin calculus approach
    • [KH01]
    • [KH01] A. KOHATSU-HIGA, Weak approximations. A Malliavin calculus approach, Math. Comp., 70 (2001), pp. 135-172.
    • (2001) Math. Comp. , vol.70 , pp. 135-172
    • Kohatsu-Higa, A.1
  • 29
    • 27644491831 scopus 로고    scopus 로고
    • On the simulation of some functionals of diffusion processes
    • [KHPOO]
    • [KHPOO] A. KOHATSU-HIGA AND R. PETTERSSON, On the simulation of some functionals of diffusion processes, Sūrikaisekikenkyūsho Kōkȳroku, 1127 (2000), pp. 153-170.
    • (2000) Sūrikaisekikenkyūsho Kōkȳroku , vol.1127 , pp. 153-170
    • Kohatsu-Higa, A.1    Pettersson, R.2
  • 30
    • 0038355030 scopus 로고    scopus 로고
    • Variance reduction methods for simulation of densities on Wiener space
    • [KHP02]
    • [KHP02] A. KOHATSU-HIGA AND R. PETTERSSON, Variance reduction methods for simulation of densities on Wiener space, SIAM J. Numer. Anal., 40 (2002), pp. 431-450.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 431-450
    • Kohatsu-Higa, A.1    Pettersson, R.2
  • 32
    • 77956845256 scopus 로고
    • Applications of the Malliavin calculus I
    • [KS84], K. Itô, ed., Kinokuniya, Tokyo
    • [KS84] S. KUSUOKA AND D. STROOCK, Applications of the Malliavin calculus I, in Stochastic Analysis, K. Itô, ed., Kinokuniya, Tokyo, 1984, pp. 271-306.
    • (1984) Stochastic Analysis , pp. 271-306
    • Kusuoka, S.1    Stroock, D.2
  • 33
    • 0004188969 scopus 로고
    • Mathematics of random phenomena: Random vibrations of mechanical structures
    • [KS86], D. Reidel, Dordrecht
    • [KS86] P. KRÉE AND C. SOIZE, Mathematics of Random Phenomena: Random Vibrations of Mechanical Structures, Math. Appl. 32, D. Reidel, Dordrecht, 1986.
    • (1986) Math. Appl. , vol.32
    • Krée, P.1    Soize, C.2
  • 35
    • 0000254487 scopus 로고
    • Stochastic differential equations and stochastic flows of diffeomorphisms
    • [Kun84], Ecole d'Eté de Probabilités de St-Flour XII, 1982, Springer-Verlag, New York
    • [Kun84] H. KUNITA, Stochastic differential equations and stochastic flows of diffeomorphisms, in Ecole d'Eté de Probabilités de St-Flour XII, 1982, Lecture Notes in Math. 1097, Springer-Verlag, New York, 1984, pp. 144-305.
    • (1984) Lecture Notes in Math. , vol.1097 , pp. 144-305
    • Kunita, H.1
  • 37
    • 0001577860 scopus 로고
    • On the convergence rates of IPA and FDC derivative estimators
    • [LP94]
    • [LP94] P. L'ECUYER AND G. PERRON, On the convergence rates of IPA and FDC derivative estimators, Oper. Res., 42 (1994), pp. 643-656.
    • (1994) Oper. Res. , vol.42 , pp. 643-656
    • L'Ecuyer, P.1    Perron, G.2
  • 39
    • 0000343766 scopus 로고    scopus 로고
    • Analysis on Wiener space and anticipating stochastic calculus
    • [Nua98] (Saint-Flour, 1995), Springer-Verlag, Berlin
    • [Nua98] D. NUALART, Analysis on Wiener space and anticipating stochastic calculus, in Lectures on Probability Theory and Statistics (Saint-Flour, 1995), Springer-Verlag, Berlin, 1998, pp. 123-227.
    • (1998) Lectures on Probability Theory and Statistics , pp. 123-227
    • Nualart, D.1
  • 40
    • 0025462369 scopus 로고
    • A general stochastic maximum principle for optimal control problems
    • [Pen90]
    • [Pen90] S. G. PENG, A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim., 28 (1990), pp. 966-979.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 966-979
    • Peng, S.G.1
  • 41
    • 0036012941 scopus 로고    scopus 로고
    • Gradient estimates for some diffusion semigroups
    • [Pic02]
    • [Pic02] J. PICARD, Gradient estimates for some diffusion semigroups, Probab. Theory Related Fields, 122 (2002), pp. 593-612.
    • (2002) Probab. Theory Related Fields , vol.122 , pp. 593-612
    • Picard, J.1
  • 47
    • 0022906632 scopus 로고
    • Sensitivity analysis via likelihood ratios
    • [RW86], J. Wilson, J. Henriksen, and S. Roberts, eds.
    • [RW86] M. I. REIMAN AND A. WEISS, Sensitivity analysis via likelihood ratios, in Proceedings of the 1986 Winter Simulation Conference, J. Wilson, J. Henriksen, and S. Roberts, eds., 1986, pp. 285-289.
    • (1986) Proceedings of the 1986 Winter Simulation Conference , pp. 285-289
    • Reiman, M.I.1    Weiss, A.2
  • 48
    • 0000427783 scopus 로고    scopus 로고
    • On the differentiation of heat semigroups and Poisson integrals
    • [Tha97]
    • [Tha97] A. THALMAIER, On the differentiation of heat semigroups and Poisson integrals, Stochastics Stochastics Rep., 61 (1997), pp. 297-321.
    • (1997) Stochastics Stochastics Rep. , vol.61 , pp. 297-321
    • Thalmaier, A.1
  • 49
    • 0000124397 scopus 로고
    • Expansion of the global error for numerical schemes solving stochastic differential equations
    • [TL90]
    • [TL90] D. TALAY AND L. TUBARO, Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Anal. Appl., 8 (1990), pp. 94-120.
    • (1990) Stochastic Anal. Appl. , vol.8 , pp. 94-120
    • Talay, D.1    Tubaro, L.2
  • 50
    • 0242467554 scopus 로고    scopus 로고
    • Approximation of quantiles of components of diffusion processes
    • [TZ04]
    • [TZ04] D. TALAY AND Z. ZHENG, Approximation of quantiles of components of diffusion processes, Stochastic Process. Appl., 109 (2004), pp. 23-46.
    • (2004) Stochastic Process. Appl. , vol.109 , pp. 23-46
    • Talay, D.1    Zheng, Z.2
  • 51
    • 0026221552 scopus 로고
    • A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems
    • [YK91]
    • [YK91] J. YANG AND H. J. KUSHNER, A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems, SIAM J. Control Optim., 29 (1991), pp.1216-1249.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 1216-1249
    • Yang, J.1    Kushner, H.J.2
  • 52
    • 0345774722 scopus 로고    scopus 로고
    • Stochastic controls: Hamiltonian systems and HJB equations
    • [YZ99], Springer-Verlag, New York
    • [YZ99] J. YONG AND X. Y. ZHOU, Stochastic Controls: Hamiltonian Systems and HJB Equations, Appl. Math. 43, Springer-Verlag, New York, 1999.
    • (1999) Appl. Math. , vol.43
    • Yong, J.1    Zhou, X.Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.