Back to Home Page

Papers 2008-2007:


  1. Dokuchaev, N. (2010) Predictability on finite horizon for processes with exponential decrease of energy on higher frequencies. Signal Processing (in press), Volume 90, Issue 2, February 2010, Pages 696-701 ( see working paper)

  2. Dokuchaev, N. (July 2009). Multiple rescindable options and their pricing. International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 04, pages 545-575

  3. Dokuchaev, N.(Aug 2008). 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 382002 (7pp) ( Fast Track Communication )

    Web-published in http://arxiv.org/abs/0708.0347

  4. Dokuchaev, N. (June 2008) .Price matching for multiple rescindable options and European options (Accepted to Applied Financial Economics Letters).

  5. Dokuchaev, N. (May 2008) Parabolic Ito Equations with Mixed in Time Conditions. Stochastic Analysis and Applications 26 iss.3, 562 – 576.

  6. Dokuchaev, N. (May 2008) Universal estimate of the gradient for parabolic equations. Journal of Physics A: Mathematical and Theoretical 41 215202 (12pt). . (Web-published in arXiv:0709.0870v6 [math.AP]).

  7. Dokuchaev, N.(August 2008) Estimates for first exit times of non-Markovian Ito processes. Stochastics 80, iss. 4, 397 – 406.

  8. Dokuchaev, N. (October 2007) Parabolic equations with the second order Cauchy conditions on the boundary..Journal of Physics A: Mathematical and Theoretical 40 No. 41, 12409-12413. . (Web-published in arXiv:0708.1978v1 [math.AP]).

  9. Dokuchaev, N. (October 2007). Maximin investment problems for discounted and total wealth. IMA J. Management Mathematics 11, no 1, 63-74.

  10. Dokuchaev, N. (Septemebr 2007). Mean-reverting market model: speculative opportunities and non-arbitrage. Applied Mathematical Finance 14, iss. 4, pages 319 – 337.

  11. Dokuchaev, N. (March 2007). Bond pricing and two unconditionally implied parameters inferred from option prices. Applied Financial Economics Letters 3, iss. 2, pp. 109-113.

  12. Dokuchaev, N. (March 2007). Discrete time market with serial correlations and optimal myopic strategies. European Journal of Operational Research 177, iss. 2, pp. 1090-1104.




Monograps

(1) Dokuchaev N.G. Mathematical finance: core theory, problems, and statistical algorithms.. January 2007, Routledge; ISBN 9780414487

(2) Dokuchaev, N.  Dynamic portfolio strategies: quantitative methods and empirical rules for incomplete information. Kluwer Academic Publishers, Boston, ISBN 0-7923-7648-X. January 2002, 232 pp. The review of this book can be found in Journal of the Operational Research Society, May 2004, vol. 55, no. 5,   pp. 555-560.

Papers of 2006 and before

Stochastic Processes and Related PDE's

(1) Dokuchaev, N. (2005). Parabolic Ito equations and second fundamental inequality.  Stochastics 77, iss. 4., pp. 349-370.

(2) Dokuchaev, N.G. Estimates for distances between first exit times via parabolic equations in unbounded cylinders, Probability Theory and Related Fields 129 (iss. 2) 2004, 290 - 314.(The original publication is available at springerlink.com).

(3) Dokuchaev, N.G. Nonlinear parabolic Ito's equations and duality approach, Theory of Probability and Applications, 48 (1) (2003),  45-62. (The original publication is available in http://epubs.siam.org/sam-bin/dbq/article/98027) (for the original in Russian: pp. 22-40).

(4) Dokuchaev, N.G. Solvability of Kolmogorov—Fokker--Planck equations for vector jump processes and occupation time on hypersurfaces. International Journal of Mathematics and Mathematical Sciences, 28:11 (2001), 637-652.

(5) Dokuchaev, N.G. Equations for distributions of the local sojourn time of a diffusion process on a surface, and control problems. Journal of Mathematical Sciences (New York) 99
(2000), no. 2, 1075-1088.

(6) Dokuchaev, N.G. Local sojourn time of diffusion and degenerating processes on a mobile surface. Th. Probab. Appl. 43 (1999), N2,
171-188. (download)

(7) Dokuchaev, N.G. Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion.  Differential equations 33 (1997), N 4, 433-442.

(8) 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.

(9) Dokuchaev, N.G. Probability distributions of Ito's processes: estimations for density functions and for conditional expectations of integral functionals. Th. Probab. Appl. 39 (1995), N 4.
662-670. (Pdf file about 1 mgb)

(10) Dokuchaev, N.G. Parabolic equations without Cauchy
conditions and control problems for diffusion processes. Part I.
Differential equations. 30 (1994), N 10, 1606-1617.

(11) Dokuchaev, N.G. Boundary value problems for functionals of Ito processes. Th.Probab. Appl. 36 (1992), N 3, 459-476. (Pdf file about 2 mgb)

(12) Dokuchaev, N.G. On moment's of first exit  forhomogeneous processes of diffusion type.   Th. Probab. Appl. 31 (1987), N 3, 3, 497-498.

Mathematical Finance

(1) Dokuchaev, N. (2006). Speculative opportunities for currency exchange under soft peg. Applied Financial Economics Letters 2, iss 6, 371-374.  http://ssrn.com/abstract=838384

(2') Dokuchaev, N. Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat
equation.  IMA J. Management Mathematics  17 (2006) 257-276. 

 (3) Dokuchaev, N. (2006). Two unconditionally implied parameters and volatility smiles and skews. Applied Financial Economics Letters 2  199-204. http://ssrn.com/abstract=550983  

(4) Dokuchaev, N. (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. (the published version)

(5) Dokuchaev, N.G., and Savkin, A.V. Universal strategies for diffusion markets and possibility of asymptotic arbitrage.  Insurance: Mathematics and Economics. Insurance Mathematics and Economics 34 (2004), iss. 3,  409-419. (The publication is available at elsevier.com). 

(6) Dokuchaev, N.G., and Savkin, A.V. A bounded risk strategy for a market with
non-observable parameters. Insurance: Mathematics and Economics,  30 (2002), 243-254.

(7) Dokuchaev, N.G., Haussmann, U. Optimal portfolio selection
and compression in an incomplete market. Quantitative Finance 1
(2001), iss. 3, 336-345 (previously presented at 1st World
Congress of Bachelier Finance Society, Paris, 2000).

(8) Dokuchaev, N.G., Zhou, X.Y. Optimal investment strategies with
bounded risks, general utilities, and goal achieving. Journal of
Mathematical Economics. 2001, 35, iss.2, 289-309.

(9) Dokuchaev, N.G. Existence of a combination of options which ensures a positive
gain. - Review of Applied and Industrial Mathematics, 2001, v.8, iss.1, 13-19.
(Publisher: Theory of Probability and its Applications).

(10) Dokuchaev, N.G., Teo, K.L. Optimal hedging strategy
for a portfolio investment problem with additional constraints.
Dynamics of Continuous, Discrete and Impulsive Systems, 2000, v.
7, 385-404.

(11) Dokuchaev, N.G., and Kyryanov V.B. Stochastic modeling of a finance market. In:
Abstracts of projects in fundamental economics supported by grants 1997-1998.
St.Petersburg University of Finance and Economics. 1999, pp. 62-65.

(12) Dokuchaev, N.G., Savkin, A.V. The pricing of options in a financial market
model with transaction costs and uncertain volatility. Journal of Multinational
Financial Management, 8 (1998), 353-364.

Back to Home Page

 

Stochastic Control 

(1) 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.

(2) Dokuchaev, N.G. and Savkin, A.V. Recursive state estimation
via limited capacity communication channels. CDC'99, pp.
4929-4932, 1999.

(3) Dokuchaev, N.G., and Zhou, X.Y. Stochastic Controls with
Terminal Contingent Conditions. Journal of Mathematical Analysis
and Applications. 238 (1999), 143-165.

(4) Dokuchaev, N.G. Optimal stopping of stochastic processes
in a problem with constraints. Th. Probab. Appl. 41 (1997), N 4.
761-768.

(5) Dokuchaev, N.G. Suboptimal damping of forced oscillations.
J. St.Petersburg University. Ser.1. (1996), iss.4, 118-122.

(6) Dokuchaev, N.G. Control of Cordes type diffusion with
partial observation and in a game problem. Differential equations
32 (1996) N 8, 1051-1062.

(7) Dokuchaev, N.G. Parabolic equations without Cauchy
conditions and control problems for diffusion processes.
Part II. Differential equations 31 (1995), N 8, 1362-1372.

(8) 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.

(9) 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.

(10) 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.

Back to Nome Page

ODE's and Electrical Networks

(1) Dokuchaev, N.G. Explicit formulae for currents at branching long
lines and for maximum of current amplitudes. IEE Proceedings.
Ser.A. V.140 (1993), N 4. 249-251. (The original publication is available at ieee.org )

(2) 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.

(3) Dokuchaev, N.G. Operation method for the boundary
value problems on graphs. Differential Equations 26 (1990), N
11, 2006-2008.

(4) 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.

 

Mathematical Education

Dokuchaev, N.G., and Kyryanov V.B. On methodology of teaching of
the stochastic finance. J. of  St.Petersburg University of Finance
and Economics. 1998, N2 (14), 153-160.

 
Back to Home Page

 

 

PRESENTATIONS 

(1) Dokuchaev, N. On $L_2$-theory of partial differential equations of mathematical physics. Physics seminar, Trent University, Ontario, July 10th, 2005.

(2) Dokuchaev, N. Some additions to the $L_2$-theory of parabolic equations and related stochastic diffusion processes. WCNA-2008, Orlando, Fl., July 2-9th, 2008.

(3) Dokuchaev, N. Myopic strategies and their optimality for stochastic discrete time market models. WCNA-2008, Orlando, Fl., July 2-9th, 2008.


(4) N.Dokuchaev, SPDEs and non-Markov Ito processes in bounded domains. York Probability Seminar. York University, Toronto., January 16th, 2008.

 (5) N.Dokuchaev. Price matching for multiple rescindable  options  and European  options.  MITACS-MCME Workshop on Risk Analysis . York University, Toronto. December 11th, 2007.

(6) Dokuchaev, N. Mathematical finance: portfolio selection and unsolved problems. Trent University, Ontario, March 28th, 2007.

(7) Dokuchaev, N. Mean-reverting market model: Novikov condition, speculative opportunities, and non-arbitrage. Seminar on Stochastic processes, Fields Institute, Toronto, March 15th, 2007.

(8) Dokuchaev, N. Dynamic portfolio selection: model choice, optimality, and uncertainty. Statistics and Actuarial Science Seminar, University College Dublin, Ireland. November 11, 2005.

(9) Dokuchaev, N. Mathematical finance: basic models and unsolved problems. Department of Mathematics and Statistics, University of Limerick, Ireland. April 22, 2005.

(10) Dokuchaev, N. Saddle points for maximin
investment problems: solution via heat equation. 57th British
Mathematical Colloquium, Liverpool, 4-7 April, 2005.

(11) 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

(12) Dokuchaev, N. Pricing rules for random
volatility with uncertainty and modeling of the volatility smile.
Toronto Probability Seminar, July 9th, 2004.


(13) 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.

(14) Dokuchaev, N.G. Dynamic portfolio strategies and filters
based on price observations, Seminar of Department of Mathematics,
London School of Economics, May 28, 2003.

(15) Dokuchaev, N.G. Investment strategies and filters based on
price observations, Probability and Finance Seminar, York
University, Toronto, July 24, 2002.

(16) 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.

(17) Dokuchaev, N.G., Haussmann, U. Optimal
portfolio selection and compression in an incomplete market. 1st
World Congress of Bachelier Finance Society, Paris, 2000.

(18) 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.

(19) 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.

(20) 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.

(21) Dokuchaev, N.G. and Savkin, A.V. The Pricing of Options in a
Financial Market Model with Transaction Costs and Uncertain
Volatility. 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).

(22) 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).

 
Back to Home Page