Novikov, Aleksandr Aleksandrovich

Total publications: 91 (77)
in MathSciNet: 75 (74)
in zbMATH: 58 (57)
in Web of Science: 41 (37)
in Scopus: 34 (33)
Cited articles: 61
Citations in Math-Net.Ru: 186
Citations in Web of Science: 275
Citations in Scopus: 276
Presentations: 5

Number of views:
This page:3453
Abstract pages:11731
Full texts:4127
Doctor of physico-mathematical sciences (1982)
Speciality: 01.01.05 (Probability theory and mathematical statistics)
Keywords: Martingales, Option Pricing, Optimal Stopping, Boundary Crossings
UDC: 519.2, 519.53, 519.24, 519.214, 519.21


Probability Theory, Stochastic Processes, Stochastic Analysis, Financial Mathematics, Statistics

Main publications:
  • 1. Novikov, A., Kordzakhia, N. "Pitman Estimators: An Asymptotic Variance Revisited" Theory of Probability and its Applications 2013.
  • 2. Novikov, A., Kordzakhia, N., Ling, T.;:" Pricing of Volume-Weighted Average Options. " Inspired by Finance" Springer, 2013
List of publications on Google Scholar

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. Alexander Gushchin, Nino Kordzakhia, Alexander Novikov, “Translation invariant statistical experiments with independent increments”, Stat. Inference Stoch. Process., 21:2 (2018), 363–383  mathnet  crossref  mathscinet  scopus (cited: 1)
2. Nino E. Kordzakhia, Yury A. Kutoyants, Alexander A. Novikov, Lin-Yee Hin, “On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion”, Statist. Probab. Lett., 139 (2018), 141–151  mathnet  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2)
3. Konstantin Borovkov, Yuliya Mishura, Alexander Novikov, Mikhail Zhitlukhin, “New and refined bounds for expected maxima of fractional Brownian motion”, Statist. Probab. Lett., 137 (2018), 142–147  mathnet  crossref  mathscinet  isi (cited: 1)  scopus

4. Konstantin Borovkov, Yuliya Mishura, Alexander Novikov, Mikhail Zhitlukhin, “Bounds for expected maxima of Gaussian processes and their discrete approximations”, Stochastics, 89:1 (2017), 21–37  mathnet  crossref  mathscinet  isi (cited: 8)  isi (cited: 8)  elib  scopus (cited: 7)
5. Nino Kordzakhia, Alexander Novikov, Bernard Ycart, “Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities”, Stat. Comput., 27 (2017), 1513 , 1523 pp.  mathnet  crossref  mathscinet  isi  elib  scopus (cited: 4)
6. A. A. Novikov, S. Alexander, N. E. Kordzahiya, T. Ling, “Pricing of asian-type and basket options via bounds”, Theory Probab. Appl., 61:1 (2017), 94–106  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus

7. A. Novikov, A. N. Shiryaev, “Discussion on “Sequential Estimation for Time Series Models” by T. N. Sriram and Ross Iaci”, Sequential Anal., 33:2 (2014), 182–185  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus (cited: 1)
8. A. A. Novikov, N. E. Kordzahia, “Lower and upper bounds for prices of Asian-type options”, Proc. Steklov Inst. Math., 287:1 (2014), 225–231  mathnet  crossref  crossref  isi (cited: 6)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 6)

9. A. Novikov, A. Shiryaev, “Remarks on moment inequalities and identities for martingales”, Statist. Probab. Lett., 83:4 (2013), 1260–1261  mathnet  crossref  mathscinet  zmath  isi  elib  scopus

10. A. A. Novikov, N. E. Kordzahiya, T. Ling, “On moments of Pitman estimators: the case of fractional Brownian motion”, Theory Probab. Appl., 58:4 (2014), 601–614  mathnet  crossref  crossref  mathscinet  isi (cited: 7)  elib  elib

11. U. Çetin, A. Novikov, A. N. Shiryaev, “Bayesian sequential estimation of a drift of fractional Brownian motion”, Sequential Anal., 32:3 (2013), 288–296  mathnet  crossref  mathscinet  zmath  isi (cited: 9)  scopus (cited: 11)
12. A. A. Novikov, N. E. Kordzakhia, “Pitman estimators: an asymptotic variance revisited”, Theory Probab. Appl., 57:3 (2013), 521–529  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 5)

13. S. Christensen, A. Irle, A. Novikov, “An elementary approach to optimal stopping problems for $\mathrm{AR}(1)$ sequences”, Sequential Anal., 30:1 (2011), 79–93  crossref  mathscinet  zmath  isi (cited: 11)  elib (cited: 7)  scopus (cited: 11)

14. G. Mititelu, Y. Areepong, S. Sukparungsee, A. Novikov, “Explicit analytical solutions for average run length of CUSUM and EWMA charts”, East-West J. Math., 2010, no. Special Vol., 253–265  mathscinet  zmath
15. J. Hinz, A. Novikov, “On fair pricing of emission-related derivatives”, Bernoulli, 16:4 (2010), 1240–1261  crossref  mathscinet  zmath  isi (cited: 11)  scopus (cited: 10)
16. K. A. Borovkov, A. N. Downes, A. A. Novikov, “Continuity theorems in boundary crossing problems for diffusion processes”, Contemporary quantitative finance, Springer, Berlin, 2010, 335–351  crossref  mathscinet  zmath

17. A. A. Novikov, “On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences”, Theory Probab. Appl., 53:3 (2009), 419–429  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 6)

18. A. N. Shiryaev, A. A. Novikov, “On a stochastic version of the trading rule “buy and hold””, Statist. Decisions, 26:4 (2008), 289–302  mathscinet  zmath
19. N. Kordzakhia, A. Novikov, “Pricing of defaultable securities under stochastic interest”, Mathematical control theory and finance, Springer, Berlin, 2008, 251–263  crossref  mathscinet  zmath  scopus
20. K. Borovkov, A. Novikov, “On exit times of Levy-driven Ornstein-Uhlenbeck processes”, Statist. Probab. Lett., 78:12 (2008), 1517–1525  crossref  mathscinet  zmath  isi (cited: 13)  scopus (cited: 14)
21. T. Schmidt, A. Novikov, “A structural model with unobserved default boundary”, Appl. Math. Finance, 15:1-2 (2008), 183–203  crossref  mathscinet  zmath  scopus (cited: 11)
22. A. Novikov, N. Kordzakhia, “Martingales and first passage times of AR(1) sequences”, Stochastics, 80:2-3 (2008), 197–210  crossref  mathscinet  zmath  isi (cited: 15)  scopus (cited: 15)

23. A. Novikov, A. Shiryaev, “On solution of the optimal stopping problem for processes with independent increments”, Stochastics, 79:3-4 (2007), 393–406  crossref  mathscinet  zmath  elib (cited: 17)  scopus (cited: 26)

24. R. Liptser, A. Novikov, “Tail distributions of supremum and quadratic variation of local martingales”, From stochastic calculus to mathematical finance, Springer, Berlin, 2006, 421–432  crossref  mathscinet  zmath

25. K. Borovkov, A. Novikov, “Explicit bounds for approximation rates of boundary crossing probabilities for the Wiener process”, J. Appl. Probab., 42:1 (2005), 82–92  crossref  mathscinet  zmath  isi (cited: 26)  elib  scopus (cited: 23)
26. A. A. Novikov, A. N. Shiryaev, “On an effective solution of the optimal stopping problem for random walks”, Theory Probab. Appl., 49:2 (2005), 344–354  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 12)  scopus (cited: 17)

27. A. A. Novikov, “Martingales and first passage times for Ornstein–Uhlenbeck processes with a jump component”, Theory Probab. Appl., 48:2 (2004), 288–303  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 14)  scopus (cited: 17)

28. A. Novikov, V. Frishling, N. Kordzakhia, “Time-dependent barrier options and boundary crossing probabilities”, Dedicated to the memory of Professor Revaz Chitashvili, Georgian Math. J., 10:2 (2003), 325–334  mathscinet  zmath

29. “Geometric Lévy Process Pricing Model”, Proc. Steklov Inst. Math., 237 (2002), 176–191  mathnet  mathnet  mathscinet  zmath
30. K. Borovkov, A. Novikov, “On a new approach to calculating expectations for option pricing”, J. Appl. Probab., 39:4 (2002), 889–895  crossref  mathscinet  zmath  scopus (cited: 24)

31. K. Borovkov, A. Novikov, “On a piece-wise deterministic Markov process model”, Statist. Probab. Lett., 53:4 (2001), 421–428  crossref  mathscinet  zmath  isi (cited: 6)  scopus (cited: 8)

32. Theory Probab. Appl., 44:3 (2000), 591–604  mathnet  crossref  crossref  mathscinet  zmath  isi

33. A. Novikov, V. Frishling, N. Kordzakhia, “Approximations of boundary crossing probabilities for a Brownian motion”, J. Appl. Probab., 36:4 (1999), 1019–1030  crossref  mathscinet  zmath
34. A. Novikov, E. Valkeila, “On some maximal inequalities for fractional Brownian motions”, Statist. Probab. Lett., 44:1 (1999), 47–54  crossref  mathscinet  zmath  isi (cited: 33)
35. A. A. Novikov, “Hedging of options with a given probability”, Theory Probab. Appl., 43:1 (1999), 135–143  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)

36. L. I. Galtchouk, A. A. Novikov, “On Wald's equation. Discrete time case”, Séminaire de Probabilités, XXXI, Lecture Notes in Math., 1655, Springer, Berlin, 1997, 126–135  crossref  mathscinet  zmath
37. A. A. Novikov, “Martingales, Tauberian theorem, and strategies of gambling”, Theory Probab. Appl., 41:4 (1997), 716–729  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 11)  scopus (cited: 12)

38. A. A. Novikov, V. V. Novikov, “Sequential procedures for multihypotheses testing”, Probability theory and mathematical statistics (Tokyo, 1995), World Sci. Publ., River Edge, NJ, 1996, 363–378  mathscinet  zmath
39. A. Le Breton, A. Novikov, “Some results about averaging in stochastic approximation”, ProbaStat '94 (Smolenice Castle, 1994), Tatra Mt. Math. Publ., 7, 1996, 255–260  mathscinet  zmath

40. A. Le Breton, A. Novikov, “Some results about averaging in stochastic approximation”, Second International Conference on Mathematical Statistics (Smolenice Castle, 1994), Metrika, 42, no. 3-4, 1995, 153–171  crossref  mathscinet  zmath  scopus (cited: 7)

41. A. Le Breton, A. A. Novikov, “Averaging for estimating covariances in stochastic approximation”, Math. Methods Statist., 3:3 (1994), 244–266  mathscinet  zmath
42. A. A. Novikov, B. A. Èrgashev, “Limit theorems for the first passage time of autoregression process over a level”, Proc. Steklov Inst. Math., 202 (1994), 169–186  mathnet  mathscinet  zmath

43. A. A. Novikov, A. N. Shiryaev, “Foreword”, Statistics and control of stochastic processes, Trudy Mat. Inst. Steklov., 202, TVP, Moscow, 1993, 3  mathnet  zmath

44. A. A. Novikov, “On the first exit time of an autoregressive process beyond a level and an application to the “change-point” problem”, Theory Probab. Appl., 35:2 (1990), 269–279  mathnet  crossref  mathscinet  zmath  isi (cited: 20)
45. A. V. Mel'nikov, A. A. Novikov, “Statistical inferences for semimartingale regression models”, Probability theory and mathematical statistics (Vilnius, 1989), v. II, “Mokslas”, Vilnius, 1990, 150–167  mathscinet

46. A. A. Novikov, “On a family of martingales connected with an autoregressive process”, Statistics and control of random processes (Preila, 1987), “Nauka”, Moscow, 1989, 160–169 (Russian)  mathscinet

47. A. V. Melnikov, A. A. Novikov, “Sequential Inferences with Prescribed Accuracy for Semimartingales”, Theory Probab. Appl., 33:3 (1988), 446–459  mathnet  crossref  mathscinet  zmath  isi (cited: 4)
48. A. A. Novikov, V. P. Dragalin, “Asymptotic expansions for 2-SPRT”, Probability theory and mathematical statistics (Kyoto, 1986), Lecture Notes in Math., 1299, Springer, Berlin, 1988, 366–375  crossref  mathscinet

49. V. P. Dragalin, A. A. Novikov, “The Asymptotic Solution of the Kiefer–Weiss Problem for Processes with Independent Increments”, Theory Probab. Appl., 32:4 (1987), 617–627  mathnet  crossref  mathscinet  zmath  isi (cited: 7)
50. V. I. Lotov, A. A. Novikov, “Asymptotic expansions in some problems of sequential testing”, Proceedings of the 1st World Congress of the Bernoulli Society (Tashkent, 1986), v. 2, VNU Sci. Press, Utrecht, 1987, 411–420  mathscinet
51. Theory Probab. Appl., 31:2 (1987), 221–232  mathnet  crossref  mathscinet  zmath  isi (cited: 8)

52. A. A. Novikov, “Consistency of least squares estimates in regression models with martingale errors”, Statistics and control of stochastic processes (Moscow, 1984), Transl. Ser. Math. Engrg., Optimization Software, New York, 1985, 389–409  mathscinet

53. A. A. Novikov, “Efficiency of selection procedures”, J. Soviet Math., 42, no. 1 (1988), 1475–1479  mathnet  crossref  mathscinet  zmath  scopus (cited: 1)

54. A. A. Novikov, “Martingale identities and inequalities and their applications in nonlinear boundary-value problems for random processes”, Math. Notes, 35:3 (1984), 241–249  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 1)

55. A. A. Novikov, “On the moment of crossing the one-sided nonlinear boundary by sums of independent random variables”, Theory Probab. Appl., 27:4 (1983), 688–702  mathnet  crossref  mathscinet  zmath  isi (cited: 7)

56. A. A. Novikov, “Small deviations of Gaussian process”, Math. Notes, 29:2 (1981), 150–155  mathnet  crossref  mathscinet  zmath  isi (cited: 6)  scopus (cited: 3)

57. A. A. Novikov, “The martingale approach in problems on the time of the first crossing of nonlinear boundaries”, Proc. Steklov Inst. Math., 158 (1983), 141–163  mathnet  mathscinet  zmath

58. A. A. Novikov, “On the exit time of sums of bounded random variables out of a curve strip”, Theory Probab. Appl., 26:2 (1982), 279–292  mathnet  crossref  mathscinet  zmath  isi (cited: 1)

59. A. A. Novikov, “A martingale approach to first passage problems and a new condition for Wald's identity”, Stochastic differential systems (Visegrád, 1980), Lecture Notes in Control and Information Sci., 36, Springer, Berlin, 1981, 146–156  crossref  mathscinet
60. A. A. Novikov, “On estimates and the asymptotic behavior of the probability of nonintersection of moving boundaries by sums of independent random variables”, Math. USSR-Izv., 17:1 (1981), 129–145  mathnet  crossref  mathscinet  zmath  isi  scopus

61. A. A. Novikov, “On conditions for uniform integrability for continuous exponential martingales”, Stochastic differential systems, Proc. IFIP-WG 7/1 Working Conf. (Vilnius, 1978), Lecture Notes in Control and Information Sci., 25, Springer, Berlin, 1980, 304–310  crossref  mathscinet
62. A. A. Novikov, “Recursive interpolation of partially observable random fields”, Mathematical statistics, Banach Center Publ., 6, PWN, Warsaw, 1980, 245–247  crossref  mathscinet

63. A. A. Novikov, “On estimates and the asymptotic behavior of nonexit probabilities of a Wiener process to a moving boundary”, Math. USSR-Sb., 38:4 (1981), 495–505  mathnet  crossref  mathscinet  zmath  isi (cited: 12)  scopus (cited: 22)

64. A. A. Novikov, “On the conditions of the uniform integrability of the continuous nonnegative martingales”, Theory Probab. Appl., 24:4 (1980), 820–824  mathnet  crossref  mathscinet  zmath  isi (cited: 8)

65. A. A. Novikov, “On stopping times of semistable diffusion processes”, Probability theory, Papers, VIIth Semester, Stefan Banach Internat. Math. Center, Warsaw, 1976, Banach Center Publ., 5, PWN, Warsaw, 1979, 203–209  crossref  mathscinet
66. A. A. Novikov, “Optimal interpolation of partially observed two-dimensional random fields”, Probability theory, Papers, VIIth Semester, Stefan Banach Internat. Math. Center, Warsaw, 1976, Banach Center Publ., 5, PWN, Warsaw, 1979, 211–220  crossref  mathscinet
67. A. A. Novikov, “On conditions for absolute continuity of probability measures”, Math. USSR-Sb., 35:5 (1979), 697–707  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus
68. A. A. Novikov, “Recurrent interpolation of partially observed random fields with discrete parameter”, Theory Probab. Appl., 23:2 (1979), 390–395  mathnet  crossref  mathscinet  zmath

69. A. A. Novikov, “On discontinuous martingales”, Theory Probab. Appl., 20:1 (1975), 11–26  mathnet  crossref  mathscinet  zmath
70. A. A. Novikov, “Martingale inequalities”, Proceedings of the School and Seminar on the Theory of Random Processes (Druskininkai, 1974), Part II, Inst. Fiz. i Mat. Akad. Nauk Litovsk. SSR, Vilnius, 1975, 89–126  mathscinet

71. A. A. Novikov, “Inequalities and identities for a certain class of martingales”, Papers presented at the Fifth Balkan Mathematical Congress (Belgrade, 1974), Math. Balkanica, 4, 1974, 465–467  mathscinet  zmath

72. A. A. Novikov, “On moment inequalities and identities for stochastic integrals”, Proceedings of the Second Japan-USSR Symposium on Probability Theory (Kyoto, 1972), Lecture Notes in Math., 330, Springer, Berlin, 1973, 333–339  crossref  mathscinet

73. A. A. Novikov, “Sequential estimation of the parameters of diffusion processes”, Math. Notes, 12:5 (1972), 812–818  mathnet  crossref  zmath  scopus (cited: 11)

74. A. A. Novikov, “On an identity for stochastic integrals”, Theory Probab. Appl., 17:4 (1973), 717–720  mathnet  crossref  mathscinet  zmath

75. A. A. Novikov, “Estimation of the parameters of diffusion processes”, Studia Sci. Math. Hungar., 7 (1972), 201–209 (Russian)  mathscinet  zmath

76. A. A. Novikov, “On moment inequalities for stochastic integrals”, Theory Probab. Appl., 16:3 (1971), 538–541  mathnet  crossref  mathscinet  zmath
77. A. A. Novikov, “On stopping times for the Wiener process”, Theory Probab. Appl., 16:3 (1971), 449–456  mathnet  crossref  mathscinet  zmath

Presentations in Math-Net.Ru
1. First passage time problems: martingale approach revised
A. A. Novikov
Conference "Stochastics, Statistics, Financial Mathematics" in honor of Professor Albert Shiryaev's 80th anniversary
October 14, 2014 14:30   
2. Lower and upper bounds for Asian-type options: a unified approach
Alexander Novikov
International conference "Advanced Finance and Stochastics"
June 24, 2013 12:10   
3. An approach to calculating the variance of Pitman estimators
A. A. Novikov, N. E. Kordzahiya
Principle Seminar of the Department of Probability Theory, Moscow State University
February 9, 2011 16:45
4. О вероятностях разорения в моделях рисков с постоянной процентной ставкой
Nino Kordzahiya, Alexander Novikov, Gurami Tsitsiashvili
Principle Seminar of the Department of Probability Theory, Moscow State University
March 31, 2010 16:45
5. Некоторые мартингальные приемы в получении точных результатов в граничных задачах для броуновского движения
A. A. Novikov, A. N. Shiryaev
Principle Seminar of the Department of Probability Theory, Moscow State University
October 26, 2005

Books in Math-Net.Ru
  1. Statistics and control of stochastic processes, Trudy Mat. Inst. Steklov., 202, ed. A. A. Novikov, A. N. Shiryaev, E. F. Mishchenko, 1993, 304 с.

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