Download 1 Working papers 2 Monographs: Mathematical Finance 3 Research

SELECTED PUBLICATIONS AND PRESENTATIONS
by Nikolai Dokuchaev
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Working papers
Recent working papers can be found and downloaded from
http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=331929
http://lanl.arxiv.org/find/math/1/au:+Dokuchaev_N/0/1/0/all/0/1
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Monographs: Mathematical Finance
Dokuchaev N.G. Mathematical finance: core theory, problems, and statistical algorithms. Rout-
ledge, January 2007, 209p.
Dokuchaev N.G. Dynamic portfolio strategies: quantitative methods and empirical rules for
incomplete information. Kluwer Academic Publishers, Boston, January 2002, 232 p.1
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Research papers ( 2011)
Dokuchaev, N. (2011). On sub-ideal causal smoothing filters. Signal Processing, accepted.
Dokuchaev, N. (2011). Mean-reverting discrete time market models: speculative opportunities
and absence of arbitrage. IMA Journal of Management Mathematics, in press.
Dokuchaev, N. (2011). On detecting the dependence of time series. Communications in Statistics – Theory and Methods, in press.
Dokuchaev, N. (2011). On the shape of the unconditionally implied volatility and forward
interest rate. Quantitative and Qualitative Analysis in Social Sciences, 5 Iss. 2 (forthcoming).
Dokuchaev, N. (2011). Option pricing via maximization over uncertainty and correction of
volatility smile. International Journal of Theoretical and Applied Finance (IJTAF) 14 (forthcoming).
Dokuchaev, N. (2011). On prescribed change of profile for solutions of parabolic equations.
Journal of Physics A: Mathematical and Theoretical 44 225204.
Dokuchaev N. (2011). Representation of functionals of Ito processes and their first exit times
Stochastics 83, No. 1, 45–66. (See also working paper at arXiv:math/0606601v2 [math.PR]
http://lanl.arxiv.org/abs/math/0606601).
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The review of this book can be found in Journal of the Operational Research Society, May 2004, vol. 55, no 5,
pp. 555-560.
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Research papers (2010)
Dokuchaev, N. (2010). Optimal strategy for gradual liquidation of equity from a risky asset.
Applied Economics Letters 17, iss. 13, 1305–1308.
Dokuchaev, N. (2010). Mean variance and goal achieving portfolio for discrete-time market
with currently observable source of correlations. ESAIM: Control, Optimisation and Calculus of
Variations 16, Number 3, 635–647.
Dokuchaev, N. (2010). Regularity for some backward heat equations, Journal of Physics A:
Mathematical and Theoretical, 43 085201.
Dokuchaev, N. (2010). Duality and semi-group property for backward parabolic Ito equations.
Random Operators and Stochastic Equations. 18, 51-72.
Dokuchaev, N. (2010). Predictability on finite horizon for processes with exponential decrease
of energy on higher frequencies. Signal Processing 90 Issue 2, February 2010, 696–701.
Dokuchaev, N. (2010). Optimality of myopic strategies for multi-stock discrete time market
with management costs. European Journal of Operational Research 200, Issue 2, 551-556.
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Research papers: Mathematical Finance
Dokuchaev, N.G. (2009). Multiple rescindable options and their pricing. International Journal
of Theoretical and Applied Finance (IJTAF), 12, Iss. 4, 545 - 575.
Dokuchaev N. (2008) Price matching for multiple rescindable options and European options.
Applied Financial Economics Letters 4, iss. 5, 319-325.
Dokuchaev, N.G. (2008). The predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters. Journal of Physics A: Mathematical and Theoretical
41 No 38, 382002 (7pp).
Dokuchaev N. (2008) Maximin investment problems for discounted and total wealth. IMA
Journal Management Mathematics 19 (1), 63–74.
Dokuchaev, N. (2007). Mean-reverting market model: speculative opportunities and nonarbitrage. Applied Mathematical Finance 14, iss. 4, 319-337.
Dokuchaev, N. (2007). Bond pricing and two unconditionally implied parameters inferred from
option prices. Applied Financial Economics Letters 3, iss. 2, 109-113.
Dokuchaev, N. (2007). Discrete time market with serial correlations and optimal myopic strategies. European Journal of Operational Research 177, iss. 2, 1090-1104.
Dokuchaev, N. (2006). Speculative opportunities for currency exchange under soft peg. Applied
Financial Economics Letters 2, 371–374.
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Dokuchaev, N. (2006) Two unconditionally implied parameters and volatility smiles and skews.
Applied Financial Economics Letters 2 199-204.
Dokuchaev, N. (2006). Saddle points for maximin investment problems with observable but
non-predictable parameters: solution via heat equation. IMA J. Management Mathematics 17
(2006) 257-276.
Dokuchaev, N.G. (2005). Optimal solution of investment problems via linear parabolic equations generated by Kalman filter. SIAM J. of Control and Optimization 44, No. 4, pp. 1239-1258.
Dokuchaev, N.G., and Savkin, A.V. (2004). Universal strategies for diffusion markets and
possibility of asymptotic arbitrage. Insurance: Mathematics and Economics 34, iss. 3, 409-419.
Dokuchaev, N.G., and Savkin, A.V. (2002). A bounded risk strategy for a market with nonobservable parameters. Insurance: Mathematics and Economics, 30, 243-254.
Dokuchaev, N.G., and Haussmann, U. (2001). Optimal portfolio selection and compression in
an incomplete market. Quantitative Finance 1, iss. 3, 336-345.
Dokuchaev, N.G., and Zhou, X.Y. (2001). Optimal investment strategies with bounded risks,
general utilities, and goal achieving. Journal of Mathematical Economics 35, iss.2, 289-309.
Dokuchaev, N.G. (2001). Existence of a combination of options which ensures a positive gain.
Surveys in Applied and Industrial Mathematics 8, iss.1, 13-19. (Scientific Publishers ”TVP”,
Moscow).
Dokuchaev, N.G., and Teo, K.L. (2000). Optimal hedging strategy for a portfolio investment
problem with additional constraints. Dynamics of Continuous, Discrete and Impulsive Systems, 7,
385-404.
Dokuchaev, N.G., and Savkin, A.V. (1998). The pricing of options in a financial market model
with transaction costs and uncertain volatility. Journal of Multinational Financial Management 8,
353-364.
Dokuchaev, N.G., and Kyryanov V.B. (1998). Methodological aspects of teaching financial
analysis. J. of St.Petersburg University of Finance and Economics 14, No. 2, 153-160.
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Research papers: Stochastic analysis
Dokuchaev N. (2008) Parabolic Ito equations with mixed in time conditions. Stochastic Analysis
and Applications 26, Iss. 3, 562–576.
Dokuchaev, N. (2008). Estimates for first exit times of non-Markovian Itô processes. Stochastics
80, 397–406.
Dokuchaev, N.G. (2008). Universal estimate of the gradient for parabolic equations. Journal
of Physics A: Mathematical and Theoretical 41, No. 21, 215202 (12pp).
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Dokuchaev, N. (2007) Parabolic equations with the second order Cauchy conditions on the
boundary Journal of Physics A: Mathematical and Theoretical. 40, pp. 12409–12413.
Dokuchaev, N. (2006) Occupation Time on Hypersurfaces for Diffusion Jump Processes. In:
”Focus on Probability Theory”, Ed. Louis R. Velle. Nova Science Publishers, NY, 2006, pp.
171-190.
Dokuchaev, N. (2005) Parabolic Ito equations and second fundamental inequality. Stochastics
77, iss. 4., pp. 349-370.
Dokuchaev, N.G. (2004) Estimates for distances between first exit times via parabolic equations
in unbounded cylinders. Probability Theory and Related Fields, 129 (2), 290 - 314.
Dokuchaev, N.G. (2003) Nonlinear parabolic Ito’s equations and duality approach, Theory of
Probability and its Applications, 48 (1), 45-62.
Dokuchaev, N.G. (1999) Local sojourn time of diffusion and degenerating processes on a mobile
surface. Theory of Probability and its Applications 43, N2, 171-188.
Dokuchaev, N.G. (1995) Probability distributions of Ito’s processes: estimations for density
functions and for conditional expectations of integral functionals. Theory of Probability and its
Applications 39, N 4. 662-670.
Dokuchaev, N.G. (1992) Boundary value problems for functionals of Ito processes. Theory of
Probability and its Applications 36 (1992), N 3, 459-476.
Dokuchaev, N.G. (1987) On moment’s of first exit for homogeneous processes of diffusion type.
Theory of Probability and its Applications 31, N 3, 3, 497-498.
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Research papers: Stochastic Control
Dokuchaev, N.G. and Savkin, A.V. A new class of hybrid dynamical systems: state estimators
with bit-rate constraints. International Journal of Hybrid Systems. 1 (2001), No 1, pp.33-50.
Dokuchaev, N.G., and Zhou, X.Y. Stochastic controls with terminal contingent conditions.
Journal of Mathematical Analysis and Applications 238 (1999), 143-165.
Dokuchaev, N.G. Optimal stopping of stochastic processes in a problem with constraints. Theory of Probability and its Applications 41 (1997), N 4. 761-768.
Dokuchaev, N.G. Suboptimal damping of forced oscillations. J. St.Petersburg University. Ser.1.
(1996), iss.4, 118-122.
Dokuchaev, N.G. Control of Cordes type diffusion with partial observation and in a game
problem. Differential equations 32 (1996), No. 8, 1051-1062.
Dokuchaev, N.G. Parabolic equations without Cauchy conditions and control problems for
diffusion processes. Part II. Differential equations 31 (1995), N 8, 1362-1372.
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Dokuchaev, N.G. and V.A.Yakubovich. Stochastic linear quadratic optimal control problem for
stationary system with quadratic constraints. J. of Computer and Systems Sciences International
32 (1994), N4, 142-152.
Dokuchaev, N.G. Solvability of analogs of Bellman equations for diffusion processes with integral
constraints and non-complete closed-loop control. Differential Equations 27 (1991), 279-288.
Dokuchaev, N.G. The integral estimations for ordinary differential equations and its application
to the non-smooth optimal control problems. Differential Equations 27 (1991), N 10. 1181-1191.
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Research papers: PDEs
Dokuchaev, N.G. Solvability of Kolmogorov–Fokker–Planck equations for vector jump pro-
cesses and occupation time on hypersurfaces. Intern. J. of Mathematics and Mathematical Sci.
28:11 (2001), 637-652.
Dokuchaev, N.G. Equations for distributions of the local sojourn time of a diffusion process
on a surface, and control problems. J. of Mathematical Sciences (New York) 99 (2000), no. 2,
1075–1088.
Dokuchaev, N.G. Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion. Differential equations 33 (1997), N 4, 433-442.
Dokuchaev, N.G. On estimates for Ito processes with discontinuous disturbances in diffusions.
In: Probability Theory and Mathematical Statistics (Proc. Kolmogorov seminars). Gordon and
Briach, London, 1996. 133-140.
Dokuchaev, N.G. Parabolic equations without Cauchy conditions and control problems for
diffusion processes. Part I. Differential equations. 30 (1994), N 10, 1606-1617.
Dokuchaev, N.G. Explicit formulae for currents at branching long lines and for maximum of
current amplitudes. IEE Proceedings. Ser.A. 140 (1993), N 4. 249-251.
Dokuchaev, N.G. The integral estimations for ordinary differential equations with a discontinuity on a domain boundary. Differential equations 28 (1992), N 11, 1540-1549.
Dokuchaev, N.G. Operation method for the boundary value problems on graphs. Differential
Equations 26 (1990), N 11, 2006-2008.
Dokuchaev, N.G. Explicit formulae for currents in branching electrical network and for the
first variation of energetic type functionals. Electromechanics (Izvestiya Vuzov. Elektromehanika)
(1990), N 2, 22-27.
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Selected Presentations
Dokuchaev, N. A Relaxed Version of the Mutual Fund Theorem. Quantitative Methods of
Finance 2010, December 15-18, Sydney, Australia.
Dokuchaev N. On volatility estimation for the high frequency stock prices. Australian Statistical
Conference, December 6-10, 2010, Fremantle, Australia.
Dokuchaev, N. SPDEs and representation theorem for non-Markov Ito processes and their first
exit times. University of Technology, Sydney, Department of Mathematics Seminar, 27 September,
2010.
Dokuchaev, N. Dimension reduction and mutual fund theorem in maximin setting for bond
market. The International Conference on Optimization and Control July 18-23, 2010, Guiyang,
China.
Dokuchaev, N. Non-parametric predictors for continuous time processes and frequency analysis.
Department of Mathematics and Statistics Seminar, Curtin University, March 10, 2010
Dokuchaev, N. Universal estimates for parabolic equations and some applications. 6th European
Conference on Elliptic and Parabolic Problems, Gaeta, Italy, May 25-29, 2009.
Dokuchaev, N. Myopic strategies and forecast errors. PIMS-UBC Probability seminar, Vancouver, April 29th, 2009
Dokuchaev, N. Reduction of impact of forecast errors and myopic portfolio strategies. 3rd
Conference on Numerical Methods in Finance, Paris, France, April 15-17, 2009.
Dokuchaev, N. On L2 -theory of partial differential equations of mathematical physics. Physics
seminar, Trent University, Ontario, July 10th, 2008.
Dokuchaev, N. Some additions to the L2 -theory of parabolic equations and related stochastic
diffusion processes. WCNA-2008, Orlando, Fl., July 2-9th, 2008.
Dokuchaev, N. Myopic strategies and their optimality for stochastic discrete time market models. WCNA-2008, Orlando, Fl., July 2-9th, 2008.
Dokuchaev, N. SPDEs and non-Markov Ito processes in bounded domains. York Probability
Seminar. York University, Toronto. January 16th, 2008.
Dokuchaev, N..
Price matching for multiple rescindable options and European options.
MITACS-MCME Workshop on Risk Analysis. York University, Toronto. December 11th, 2007.
Dokuchaev, N. Mathematical finance: portfolio selection and unsolved problems. Trent University, Ontario, March 28th, 2007.
Dokuchaev, N. Mean-reverting market model: Novikov condition, speculative opportunities,
and non-arbitrage. Seminar on Stochastic processes, Fields Institute, Toronto, March 15th, 2007.
Dokuchaev, N. Dynamic portfolio selection: model choice, optimality, and uncertainty. Statis-
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tics and Actuarial Science Seminar, University College Dublin, Ireland. November 11, 2005.
Dokuchaev, N. Saddle points for maximin investment problems: solution via heat equation.
57th British Mathematical Colloquium, Liverpool, April 4-11, 2005.
Dokuchaev, N. Parabolic equations in unbounded cylinders and estimates for distances between
first exit times. Seminar of School of Mathematical Sciences, Dublin City University. November
17th, 2004.
Dokuchaev, N. Pricing rules for random volatility with uncertainty and modeling of the volatility
smile. Toronto Probability Seminar, July 9th, 2004.
Dokuchaev, N.G. Estimates for distances between first exit times via parabolic equations in
unbounded cylinders. Probability and Finance Seminar, York University, Toronto, July 27, 2003.
Dokuchaev, N.G. Dynamic portfolio strategies and filters based on price observations, Seminar
of Department of Mathematics, London School of Economics, May 28, 2003.
Dokuchaev, N.G. Investment strategies and filters based on price observations, Probability and
Finance Seminar, York University, Toronto, July 24, 2002.
Dokuchaev, N.G. Explicit optimal solution in maximin setting for investment problems with totally unhedgeable coefficients. European Investment Review Conference. Paris, France. September
20-21, 2001.
Dokuchaev, N.G., Haussmann, U. Optimal portfolio selection and compression in an incomplete
market. 1st World Congress of Bachelier Finance Society, Paris, 2000.
Dokuchaev, N.G., Haussmann, U. Adaptive Portfolio Selection Based on Historical Prices.
Quantitative Risk Management in Finance. Carnegie Mellon University, Pittsburgh. July 31 August 5, 2000.
Dokuchaev, N.G. and Savkin, A.V. Recursive state estimation via limited capacity communication channels. CDC’99, pp. 4929-4932, 1999.
Dokuchaev, N.G. and Zhou, X.Y. Stochastic controls of backward stochastic differential equations. CDC’99, pp. 1470-1475, 1999.
Dokuchaev, N.G. and Savkin, A.V. A hedging investment strategy with a positive average
gain without market estimation. In: Proc. of CESA’98 Symposium on Applied Mathematics and
Optimization. Tunisia, 1998.
Dokuchaev, N.G. and Savkin, A.V. Asymptotic arbitrage in a stochastic financial market model.
In: Proc. of CESA’98 Symposium on Applied Mathematics and Optimization. Tunisia, 1998.
Dokuchaev, N.G. and Savkin, A.V. The Pricing of Options in a Financial Market Model with
Transaction Costs and Uncertain Volatility. In: 10th Annual Australasian Finance and Banking
Conference, Sydney, NSW, Refereed Proceedings. School of Banking and Finance, University of
New South Wales, 1: pp. 121-134 (1997).
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Dokuchaev, N.G. and Savkin, A.V. Asymptotic arbitrage in a financial market model based on
the historical volatility. In: 10th Annual Australasian Finance and Banking Conference, Sydney,
NSW, Refereed Proceedings. School of Banking and Finance, The University of New South Wales,
1: pp. 113-120 (1997).
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