..................................Publications

Stochastic Calculus, Extended Stochastic Integrals

1. Representation of functionals of Wiener and Poisson processes as stochastic
integrals. Probab. Theory and Its Appl., 18, 2, 1973.

2. Integral representation for functionals of the processes with independent
increments. Probab. Theory and Its Appl., 19, 4, 1974.

3. Generalized Ito formula for an extended stochastic integral on the Poisson
random measure. Uspekhi Mat. Nauk, 29, 4, 1974.

4. Extended stochastic integrals. Proceedings of the School-Seminar on
the Theory of Random Processes. Druskininkai, November 25-30, 1974.
Part I. Vilnius, 1975. With A.V. Skorokhod. English translation: (392 Ko)

5. On extended stochastic integrals. Probab. Theory and Its Appl., 20,4, 1975.

6. On the question of absolute continuity and singularity of probability
measures. Mat. Sbornik, 104, 2, 1977. English translation: Math.
USSR Sbornik, 33, 2, 1977. With R.Sh. Liptser and A.N. Shiryaev.

7. "Predictable" criteria for absolute continuity and singularity of probability
measures (the continuous time case). Dokl. Akad. Nauk SSSR,
237, 5, 1977. English translation: Soviet Math. Dokl., 18, 6, 1977,
pp.1515-1518. With R.Sh. Liptser and A.N. Shiryaev.

8. Absolute continuity and singularity of locally absolute continuous probability
distributions. Part I: Mat. Sbornik, 107, 3, 1978. Part II: Mat.
Sbornik, 108, 1, 1979. English translation: Math. USSR Sbornik, 35,5,
1979, 36, 1, 1980. With R.Sh. Liptser and A.N. Shiryaev.

9. On absolute continuity of probability measures for Markov-Ito processes.
Lecture Notes in Control and Information Science, 1980.
With R.Sh. Liptser and A.N. Shiryaev.

10. On the representation of integer-valued random measures and local
martingales by means of random measures with deterministic compensators.
Mat. Sbornik, 111, 2, 1980.
English translation: Math. USSR Sbornik, 39, 2, 1981.
With R.Sh. Liptser and A.N. Shiryaev.

11. On the proximity in variation of probability measures. Dokl. Akad.
Nauk SSSR, 278, 2, 1984. English translation: Soviet Math. Dokl., 30,2, 1984.
With R.Sh. Liptser and A.N. Shiryaev.

12. An estimate of closeness in variation of probability measures.
Probab. Theory and Its Appl., 30, 2, 1985.

13. On the variation distance for probability measures defined on a filtered
space. Probab. Theory and Related Fields, 71, 1986.
With R.Sh. Liptser and A.N. Shiryaev.

14. Contiguity of distributions of multivariate point processes. Lecture
Notes in Math., 1299, 1988.

Point Processes

15 . Martingale methods in the theory of point processes. Proceedings of
the School-Seminar on the Theory of Random Processes. Druskininkai,
November 25-30, 1974. Part II. Vilnius, 1975.
With R. Sh. Liptser and A.N. Shiryaev.

16. Criteria of absolute continuity of measures corresponding to multivariate
point processes. Lecture Notes in Math., 550, 1976.
With R.Sh. Liptser and A.N. Shiryaev.

17. Necessary and sufficient conditions for absolute continuity of measures
corresponding to point (counting) processes. Proceedings of the International
Symposium on Stochastic Differential Equations. Kyoto, 1976.
With R.Sh. Liptser and A.N. Shiryaev.

18. The capacity of a channel of the Poisson type.
Probab. Theory and Its Appl., 23, 1, 1978.

19. A note on the Burke-Brémaud theorem on the output process.
In.: Probabilistic Methods in a Control Problems for Economical Processes.
CEMI, 1979.

20. An example of application of general criteria of absolute continuity for
counting processes. In: Multivariate Statistical Analysis. CEMI, 1979.

21. Some limit theorems for simple point processes. A martingale approach.
Stochastics, 1980, 3, p. 203-216.
With R.Sh. Liptser and A.N. Shiryaev.

22. Weak and strong convergence of distributions of counting processes.
Probab. Theory and Its Appl., 28, 2, 1983.
With R.Sh. Liptser and A.N. Shiryaev.

23. On the rate of convergence of the distributions of counting processes to
the distribution of the counting process with independent increments.
Dokl. Akad. Nauk SSSR, 264, 5, 1982.

24. On convergence in variation of the distributions of multivariate point
processes. Z.Wahrscheinlichkeitstheorie verw. Gebiete, 63, 1983.
With R.Sh. Liptser.

25. On the proximity of counting processes to counting processes with independent
increments. In: "Statistics. Probability. Economics", Nauka,1985.

26. On the probabilistic representation of a solution of the telegraph equation.
Probab. Theory and Its Appl., 37, 2, 1992.

27. On a closed queueing system. Soobshch. Akad. Nauk Gruz. 152
(1995), 3, 465-469. With G.L. Arsenishvili.

28. A higher order approximation in convergence of distributions of the
Cox processes with fast Markov switchings. Stochastics and Stochastics
Reports, 54, pp. 211-219, 1995. With G.B. Di Masi.



Stochastic Control

29. On necessary conditions of optimality in a control problem of a random
process. In: Modeling of Technological Progress and Control of
Economical Processes under Incomplete Information, CEMI, 1976.

30. On the Pontryagin maximum principle for linear stochastic differential
equations. In: Probabilistic Models and Control of Economical
Processes, CEMI, 1978, pp. 85-94. (1.8 Mo)

31. On an existence of the optimal solution in a control problem for a
counting process. Mat. Sbornik, 119, 3, 1982.

32. Optimal control of singularly perturbed linear systems. Stochastics and
Stochastics Reports, 1991, 32. With S.M. Pergamenshchikov.

33. On optimal control of singularly perturbed stochastic differential equations.
In: Modelling, Estimation and Control of Systems with Uncertainty.

Eds. G.B. Di Masi, A. Gombani, A.B. Kurzhansky. Birkhauser,
1991. With S.M. Pergamenshchikov.

34. On the sets of attainability for controlled stochastic differential equations.
Uspekhi Mat. Nauk, 45, 1, 1991. With S.M. Pergamenshchikov.

35. On control of two-scale stochastic systems with linear dynamics in fast
variables. Mathematics of Control, Signals, and Systems, 9 (1996), pp.107-122.
With W. Runggaldier.

36. On sensitive probabilistic criteria for LQG problem with infinite horizon.
Obozreniye Prikladnoi i Promyshlennoi matematiki, 5 (1998), 2,410-422.
With G.B. Di Masi.

37. On the convergence of attainability sets for controlled two-scale stochastic
linear systems. SIAM Journal on Control and Optimization, 1, 1997.
With S.M. Pergamenshchikov.

38. On the Pontryagin maximum principle for SDEs with Poisson type
disturbances. Statistics and Control of Random Processes. Proceedings
of Steklov Mathematical Institute Seminar. The Liptser Festschrift.
World Scientific, 1997, 173-190 (217 Ko)

39. On a stochastic optimality of the feedback control in the LQG-problem.
Probability Theory and Its Applications, 4, 2003.
With T. Belkina and E.L. Presman.



Stochastic Differential Equations

40. On singularly perturbed stochastic equations and partial differential
equations. Dokl. Akad. Nauk SSSR, 311, 5, 1990. English translation:
Soviet Math. Dokl., 41, 2, 1990. With S.M. Pergamenshchikov.

41. Singular perturbations of stochastic differential equations: the Tikhonov
theorem. Mat. Sbornik, 1990, v.191, 9, p. 1170-1182. English translation:
Math. USSR Sbornik, 71, 1, 1992. With S.M. Pergamenshchikov.

42. Asymptotic expansions for singularly perturbed stochastic differential
equations. In: New Trends in Probability and Statistics. Vol. 1.
Eds. V.V. Sazonov, T.L. Shervashidze. Mokslas/VSP, Vilnius, Utrecht,
1991. With S.M. Pergamenshchikov and S.M. Stoyanov.

43. The strong convergence of two-scale stochastic systems and singular
perturbations of filtering equations. J. of Math. Systems, Estimation,
and Control, n.2, 1993. With G.B. Di Masi.

44. Large deviations for solutions of singularly perturbed stochastic differential
equations. Uspekhi Mat. Nauk, 5, 1995. With S.M. Pergamenshchikov.


Mathematical Economics and Mathematical Finance

45. A stochastic model of a developping production. In: Probabilistic Models
and Control of Economical Processes, CEMI, 1978, pp. 74-84. (1.9 Mo)

46. A stochastic modification of the von Neumann-Gale model of an expanding
economy: a turnpike theorem. Institute of Computer Sciences
Reports, Warsawa, 1979, n. 359. With I.V. Evstigneev.

47. On existence of the equilibrium in the stochastic von Neumann-Gale
model. In: Multivariate Statistical Analysis. CEMI, 1979.
With I.V. Evstigneev.

48. On a stochastic modification of the von Neumann-Gale model. Uspekchi
Mat. Nauk, 35, 4, 1980. With I.V. Evstigneev.

49. Stochastic models of the economic growth and equilibria. Chapter in
the book: Mathematical Tools of Economical Modeling, Nauka, 1983.
With I.V. Evstigneev, P.K. Katyshev, S.E. Kuznetsov.

50. Estimation of parameters of systems of simultaneous equations. Chapter
in: S.A. Aivazyan, I.S. Yenyukov, L.D. Meshalkin. Applied Statistics.
V.2. Study of Relationships. Finansy i Statistica. Moscow, 1985.

51. Hedging of options on stocks with Markov volatilities. Probab. Theory
and Its Appl., 1, 1994. With G.B. Di Masi and W. Runggaldier.

52. Large financial markets: asymptotic arbitrage and contiguity. With D.
Kramkov. Probab. Theory and Its Appl., 1,1994.

53. On the pricing of options of European and American type. Discrete
time. Probability Theory and Its Applications, 1, 1994.
With A.N. Shiryaev, D.O. Kramkov, A.V. Melnikov.

54. On the pricing of options of European and American type. Continuous
time. Probability Theory and Its Applications, 1, 1994.
With A.N. Shiryaev, D.O. Kramkov, A.V. Melnikov.

55. No-arbitrage and equivalent martingale measures: an elementary proof
of the Harrison-Pliska theorem. Probab. Theory and Its Appl., 3,1994.
With D. Kramkov.

56. Bond markets where prices are driven by a general marked point process.
Stockholm School of Economics. Working Paper n. 47, 1995.
With T. Björk and W. Runggaldier.

57. Bond market structure in the presence of marked point processes. Mathematical
Finance, 7, 2, 1997, p. 211-239. With T. Björk and W. Runggaldier.

58. Optional decompositions in discrete time. Atti del convegno in onore
di Oliviero Lessi. Università degli Studi di Padova, 1997, 47-68.
With H. Föllmer.

59. Towards a general theory of bond markets. Finance and Stochastics,
1 (1997), p. 141-174. With T. Björk, G.B. Di Masi, and W. Runggaldier. (289 Ko)

60. On Leland’s strategy of option pricing with transaction costs. Finance
and Stochastics, 1, 3, 1997, 239-250. With M. Safarian.(146 Ko)

61. On the FTAP of Kreps-Delbaen-Schachermayer. Statistics and Control
of Random Processes. The Liptser Festschrift. Proceedings of
Steklov Mathematical Institute Seminar, World Scientific, 1997, 191-203. (231 Ko)

62. Optional decomposition and Lagrange multipliers. Finance and Stochastics,
2, 1, 1998, 69-81. With H. Föllmer. (149 Ko)

63. Asymptotic arbitrage on large financial markets. Finance and Stochastics,
2, 2, 1998, 143-172. With D. Kramkov.

64. Hedging and liquidation under transaction costs in currency markets.
Finance and Stochastics, 3 (1999), 2, 237-248.

65. Louis Bachelier: To the centenary of Théeorie de la Spéculation. Mathematical
Finance. 10 (2000), 3, 341-353.
With J.-M. Courtault, B. Bru, P. Crepel, I. Lebon, A. Le Marchand. (356 Ko)

66. Hedging under transaction costs in currency markets: a discrete-time
model. Mathematical Finance, 12 (2002), 1, 45-61.
With F. Delbaen and E. Valkeila.(263 Ko)

67. Hedging under transaction costs in currency markets: a continuoustime
model. Mathematical Finance, 12 (2002), 1, 63-70. With G. Last.

68. The Harrison-Pliska arbitrage pricing theorem under transaction costs.
Journal of Mathematical Economics, 35 (2001), 2, 185-196.
With Ch. Stricker. (143 Ko)

69. Hedging in a model with transaction costs. Proceedings of Steklov
Institute of Mathematics, 237, 2002, 208-214. With G. Last.

70. On equivalent martingale measures with bounded densities. Séminaire
de Probabilités XXXV, Lect. Notes in Math., 1755, 2001, 139-148.
With Ch. Stricker. (166 Ko)

71. A teachers’ note on no-arbitrage criteria. Séminaire de Probabilités
XXXV, Lect. Notes in Math., 1755, 2001, 149-152. With Ch. Stricker.(81 Ko)

72. Arbitrage theory. In: Handbooks in Mathematical Finance. Option
Pricing: Theory and Practice. Cambridge University Press, 2001, 3-42. (275 Ko)

73. Option pricing by large risk aversion utility under transaction costs.
Decisions in Economics and Finance, 24, 2002, 2, 127-136.
With B. Bouchard, N. Touzi .(71 Ko)

74. On the optimal portfolio for the exponential utility maximization: remarks
to the six-author paper. Mathematical Finance, 12 (2002), 2,125-134.
With Ch. Stricker.(185 Ko)

75. In the insurance business risky investments are dangerous. Finance
and Stochastics, 6 (2002), 2, 227-235.
With A.G. Frolova and S.M. Pergamenshchikov. (162 Ko)

76. No-arbitrage criteria for financial markets with efficient friction. Finance
and Stochastics, 6 (2002), 3, 371-382.
With M. Rasonyi and Ch. Stricker.

77. Hedging of contingent claims under transaction costs. Advances in
Finance and Stochastics. Eds. K. Sandmann and Ph. Schönbucher,
Springer, 2002, p. 125-136. With Ch. Stricker.

78. On the true submartingale property, d'après Schachermayer. Séminaire
de Probabilités XXXVI, Lect. Notes in Math., 1801 (2002), 413-415.
With Ch. Stricker.(160 Ko)

79. On a closedness of sums of convex cones in L0 and the robust noarbitrage
property. Finance and Stochastics, 7 (2003), 3, 403-411.
With M. Rasonyi and Ch. Stricker. (160 Ko)

80. A geometric approach to portfolio optimization in models with transaction
costs. Finance and Stochastics, 8 (2004), 2, 207-227.
With C. Klueppelberg.

81. Remarks on the true no-arbitrage property. Séminaire de Probabilités,
XXXVIII, Lect. Notes in Math., 1857 (2005), 186-194.
With Ch.Stricker. (169 Ko)

82. On the law of one price. Finance and Stochastics. 8 (2004), 4, 525-530.
With J.-M. Courtault, F. Delbaen, and Ch. Stricker. (113 Ko)

83. The Dalang-Morton-Willinger theorem under delayed and restricted
information. Séminaire de Probabilités, Lect. Notes in Math., (2006).
With Ch. Stricker. (239 Ko)

84. A consumption-investment problem with production possibilities. From
Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift,
Springer-Verlag, 2006, 315-332. With M. Kijima.(233 Ko)

85. Multiparameter generalizations of the Dalang-Morton-Willinger theorem.
From Stochastic Calculus to Mathematical Finance. The Shiryaev
Festschrift, Springer-Verlag, 2006, 333-341.
With Yu. Mishura and L. Sakhno.(168 Ko)

86. A positive interest rate model with sticky barrier. Qualitative Finance,
7 (2007), 3, 269--284. With M. Kijima and S. Rinaz. (143 Ko)

87. No-arbitrage properties for financial markets with transaction costs and
incomplete information. Finance and Stochastics, 11 (2007), 2, 237-251.
With D. De Valliére and Ch. Stricker. (219 Ko)

88. Mean square error for the Leland-Lott hedging strategy.
In: Recent Advances in Financial Engineering: Proceedings of the 2008 Daiwa
International Workshop on Financial Engineering. World Scienific, 2009.
With Moussa Gamys. (267 Ko)

89. On martingale selectors of cone-valued processes. Séminaire
de Probabilités XLI, Lect. Notes in Math. 1934, Springer, 2008, 437-442.
With Ch. Stricker. (154 Ko)

90. In discrete time a local martingale is a martingale under an
equivalent probability measure. Finance and Stochastics, 12 (2008), 3, 293-297.
(148 Ko)

91. Hedging of American options under transaction costs.
Finance and Stochastics, 13 (2009), 1, 105-119.
With D. De  Valliére and E. Denis.(212 Ko)

92. Mean square error for the Leland-Lott hedging strategy: convex pay-offs.
Finance and Stochastics, 14 (2010), 4, 625-667. With Emmanuel Denis. (327 Ko)

93. Consistent price systems and arbitrage opportunities of the second
kind in models with transaction costs.
Finance and Stochastics, 16 (2012), 135-154. With Emmanuel Denis (Lépinette). (213 Ko)

94. Consumption-investment problem with transaction costs
for Lévy-driven price processes.
Finance and Stochastics, 20 (2016), 3, 705-740. With Dimitri De  Vallière. (259 Ko)

95. Small transaction costs, absence of arbitrage and consistent price systems.
Finance and Stochastics, 16 (2012), 3, 357-368. With Julien Grépat. (147 Ko)

96. Essential supremum with respect to a random partial order.
Journal of Mathematical Economics, 49 (2013), 6, 478-487. With Emmanuel Lépinette. (467 Ko)

97. Essential supremum and essential maximum with respect to random
preference relations.
Journal of Mathematical Economics, 49 (2013), 6, 488-495. With Emmanuel Lépinette. (303 Ko)

98. On supremal and maximal sets with respect to random partial orders.
IIn: "Set Optimization - State of the Art and Applications in Finance". Eds: Hamel A.H., Loehne A., Heyde F., Rudloff B., Schrage C. Springer, 2015, 275-292. With Emmanuel Lépinette. (397 Ko)

99. Viscosity solutions of integro-differential equations for non-ruin probabilities.
Theory of Probability and Its Applications, 60 (2015), 4, 802-810. With T. Belkina. (234 Ko)

100. In the insurance business risky investments are dangerous: the case of negative risk sums.
Finance and Stochastics, 20 (2016), 2, 355-379. With Serguei Pergamenshchikov. (299 Ko)

101. On local martingale deflators and market portfolios.
Finance and Stochastics, 20 (2016), 4, 1097-1108. With Kostas Kardaras and Shiqi Song. http://arxiv.org/abs/1501.04363

102. Ruin probabilities for a Levy-driven generalised Ornstein-Uhlenbeck process. Finance and Stochastics, 24 (2020), 1, 39-69. With Serguei Pergamenshchikov. (452 Ko)

103. Clearing in financial networks.
Theory of Probability and Its Applications, 62 (2017), 2, 311-344. With Khalil El Bitar and Rita Mokbel. (401 Ko)

104. On uniqueness of clearing vectors reducing the systemic risk.
Informatics and Applications, 11 (2017), 1, 109-118. With Khalil El Bitar and Rita Mokbel. (475 Ko)

105. Dynamic models of systemic risk and contagion.
Informatics and Applications, 11 (2017), 2, 2-14. With Khalil El Bitar and Rita Mokbel. (758 Ko)

106. On a multi-asset version of the Kusuoka limit theorem: convergence of hedging sets.
Finance and Stochastics, 25 (2021), 167-187. With Julien Grépat. (341 Ko)

107. On sets of laws of continuous martingales.
Theory of Probability and Its Applications, 65 (2020), 4. (Rus. 319 Ko), (216 Ko)

108. Ruin probabilities with investments: smoothness, IDE and ODE, asymptotic behavior. With Nikita Pukhlyakov.

109. Ruin probabilities for a Sparre Andersen model with investments. With Ernst Eberlein and Thorsten Schmidt.

110. On ruin probabilities with risky investments in a stock with stochastic volatility.
Extremes (2021). With Anastasia Ellanskaya.