Stochastic Systems and Modelling of Financial Markets  Page description

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Details of project

  
Identifier
47193
Type K
Principal investigator Gerencsér, László
Title in Hungarian Sztochasztikus Rendszerek és Pénzügyi Piacok Modellezése
Title in English Stochastic Systems and Modelling of Financial Markets
Panel Informatics and Electrical Engineering
Department or equivalent HUN-REN Institute for Computer Science and Control
Participants Berlinger, Edina
Gerencsérné Vágó, Zsuzsanna
Mátyás, Zalán
Michaletzky, György
Molnár Sáska, Gábor
Orlovits, Zsanett
Rásonyi, Miklós
Sándorné Kmecs, Ildikó
Száz, János
Szepesvári, Csaba
Véber, Miklós
Starting date 2004-01-01
Closing date 2006-12-31
Funding (in million HUF) 8.291
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
A kutatások célja a sztochasztikus rendszerek legkorszerűbb módszereinek az alkalmazása a pénzügyi piacok modellezésében és maguknak a módszereknek a továbbfejlesztése. A pénzügyi matematika ma egyik legnagyobb kihívása jó fedezeti stratégiák kialakítása nem-teljes piacokon. Ez matematikailag egy sajátos sztochasztikus adaptív kontrol problémát jelent, ahol a dinamikát egy sokdimenziós switching diffúziós folyamat írja le. Ehhez az általános problémához számos részprobléma köthető. . Kutatásaink javarészt PhD hallgatók által is megoldható módszertani problémákhoz kötődnek. A fő területek: rejtett Markov-folyamatok, tőzsdemodellek, sztochasztikus volatilitás, valamint a kontroll elmélet és az opcióárazás kapcsolata. Ezen túl munkáinkban a sztochasztikus adaptív kontrol néhány alapvető kérdését is vizsgáltuk.
Results in English
The objective of this research was to apply and develop advanced methods of stochastic systems for modelling financial markets. A current challenge in financial mathematics is the development of reliable hedging strategies for incomplete markets. Mathematically this is a stochastic asptive control problem in which the dynamics of the system is described by a multivariable switching diffusion process. This major problem could be related to a number of simpler problems. Most of our research topics were releated to technical problems that could be handled within the framework of a PhD program. The main areas were: hidden Markov models, models for a stock exchange, stochastic volatility and the relationship between stochastic control and option pricing. In addition we have studied a few fundamental problems of stochastic adaptiv control.
Full text http://real.mtak.hu/1725/
Decision
Yes





 

List of publications

  
GERENCSÉR, L. - HJALMARSSON, H.: Adaptive input design for ARX systems, Proc. of the European Control Conference, ECC’06, Kos, Greece, July 2-5, 2007., 2007
GERENCSÉR, L. – MÁTYÁS, Z.: A behavioral stock market model, In: Proc. of the International Conference on Stochastic Finance, Lisbon, Portugal, September 26-30, (electronic), 2004
GERENCSÉR, L. – MOLNÁR-SÁSKA, G.: Change detection of Hidden Markov Models, In: Proc. of the 43rd IEEE Conference on Decision and Control, Nassau, The Bahamas, December 14-17, 2004, WeA11.2, 2004
GERENCSÉR, L. – HILL, S.D. - VÁGÓ, Zs. – VINCZE, Z.: Discrete optimization, SPSA and Markov Chain Monte Carlo methods, In: Proc. of the American Control Conference, Boston, MA, USA, June 30 - July 2, 2004, ThP17, pp. 3814-3819, 2004
HILL,S. D. – GERENCSÉR,L. - VÁGÓ,Zs.: Stochastic Approximation on Discrete Sets Using Simultaneous Perturbation Difference Approximations, In: Proc. of theAmerican Control Conference 2004, June 30- July 2, 2004, Boston, MA, USA, ThM06, pp. 2795-2798, 2004
GERENCSÉR,L. – RÁSONYI, M.-VÁGÓ,Zs.: Controlled Lyapunov-Exponents with Applications, In: Proc. of the 43rd IEEE Conference on Decision and Control, Nassau, The Bahamas, December 14-17 2004, WeC08, 2004
RÁSONYI, M: Utility maximization in discrete-time financial market models, In: Proc. of the International Conference on Stochastic Finance, Lisbon, Portugal, September 26-30, 2004, (electronic), 2004
RÁSONYI, M.: Arbitrage theory and risk-neutral measures, Decisions in Economics and Finance, vol. 27, no. 2, pp. 109-123, 2004., 2004
RÁSONYI, M.: Arbitrázs nagy pénzügyi piacokon, Szigma, vol. 35, no. 3-4, pp. 123-130, 2004, 2005
GERENCSÉR, L. MOLNÁR-SÁSKA, G.: Identification of hidden Markov models - uniform LLN-s, Modeling, Estimation and Control: Festschrift in honor of Giorgio Picci, 2007
GERENCSÉR, L. , VÁGÓ, Zs.: The Mathematics of Noise-Free SPSA Stochastic Approximation with Vanishing Random Fields, átdolgozás alatt, IEEE Trans. Automatic Control, 2007
GERENCSÉR, L. - MICHALETZKY, Gy. - VÁGÓ, Zs.: Risk-sensitive identification of linear stochastic systems, Mathematics of Control, Signals and Systems, vol 27, no 2, pp. 77-100, 2005
SZEIDL, Á. – GERENCSÉR, L. – MICHALETZKY, Gy.: Quantized Gaussian ARMA identification, Systems and Control Letters, közlésre elfogadva, 2005
GERENCSÉR, L.: A representation theorem for recursive estimators, SIAM Journal on Control and Optimization, 44 (2005), pp. 2123-2188, 2005
CARASSUS, L. – RÁSONYI, M.: Convergence of utility indifference prices to the superreplication prices to the super-replication price, Mathematical Methods of Operations Research, vol. 64, pp. 145-154, 2006, 2006
FINESSO, L. - GERENCSÉR, L. – KMECS, I.-SZILÁGYI, T.: Estimation of quantized Gaussian linear models - a randomized EM method, Int. Journal of Adaptive Control and Signal Processing Control, átdolgozás alatt, 2006
BERLINGER, E. – GERENCSÉR, L. – MÁTYÁS, Z. – RÁSONYI, M.: Analysis of an income-contingent student loan system, The Economics of Transition, benyújtás előtt, 2006
GERENCSÉR, L. – HILL, S.D. – VÁGÓ, Zs.: Discrete Stochastic Approximation Via Simultaneous Difference Approximations, In: Proc. of the American Control Conference, Portland, Oregon, USA, June 8 - 10, 2005, pp. 307-308, 2005
GERENCSÉR, L. – HJALMARSSON, H.: Adaptive input design in system identification, In: Proc. of the 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC’05, Seville, Spain, December 12-15, 2005, WeB04.4, 4988-4993, 2005
GERENCSÉR, L. – MÁTYÁS, Z. – SZÁZ, J.: A stochastic feedback system model of a stock exchange., In: Proc. of the 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC’05, Seville, Spain, December 12-15, 2005, WeB11.1, pp. 5215-5, 2006
GERENCSÉR, L.– MÁTYÁS, Z.: Almost sure convergence of stochastic appoximation algorithms with resetting, IEEE Trans. on Information Theory, benyújtás előtt, 2006
GERENCSÉR, L. - MICHALETZKY, Gy. - ORLOVITS, Zs.: On the Top-Lyapunov Exponent of Block-triangular Stationary Random Matrices, Proc. of the European Control Conference, ECC’07, Kos, Greece, July 2-5, 2007, accepted for publication., 2007
GERENCSÉR, L. – MICHALETZKY, Gy. – MOLNÁR-SÁSKA, G.: Improved estimation of the exponential stability of the predictive filter in Hidden Markov Models, American Control Conference, ACC 2006, Minneapolis, Minnesota, USA, June 14-16, 2006, FrB08.5, pp. 5177- 5182., 2006
GERENCSÉR, L. – MICHALETZKY, Gy. – ORLOVITS, ZS.: On the top Lyapunov-exponent of block-tringular stationary random matrices, Systems and Control Letters, közlésre benyújtva, 2007
GERENCSÉR, L. – MOLNÁR-SÁSKA, G. – ORLOVITS, Zs.: Recursive estimation of Hidden Markov Models, In: Proc. of the 44th IEEE Conference on Decision and Control and European Control Conference CDC-ECC’05, Seville, Spain, December 12-15, 2005. MoB16.3, pp. 1209-12, 2005
GERENCSÉR, L. – RÁSONYI, M. – SZEPESVÁRI, Cs. – VÁGÓ, Zs.: Log-optimal portfolios and control Lyapunov-exponents, In : Proc. of the 44th Conference on Decision and Control and European Control Conference, CDC-ECC'05, Seville, Spain, December 12-15, 2005, MoC11.4, pp. 1764-1769, 2005
MOLNÁR-SÁSKA, G.: Statistical Analysis of Hidden Markov Models, PhD Doktori Értekezés, 2005
STETTNER, L. - RÁSONYI,M.: On utility maximization in discrete-time market models, Annals of Applied Probability, vol. 15, no. 2, pp. 1367-1395, 2005
GERENCSÉR, L. – MOLNÁR-SÁSKA, G. – ORLOVITS, Zs.: Change-detection of Hidden Markov Models and GARCH processes, In: Proc. of the International Conference on Stochastic Finance, Lisbon, Portugal, September 26-30, 2004, (electronic), 2005
GERENCSÉR, L.: A representation theorem for recursive estimators, Proc. of 45th IEEE Conference on Decision and Control CDC’06, San Diego, California, USA, December 13-15, 2006, WeA09.5, Stochastic Systems I (SIAM), pp. 320-325, 2006
GERENCSÉR, L. – MOLNÁR-SÁSKA, G. – MICHALETZKY, - GY TUSNÁDY, G.: New methods for the statistical analysis of Hidden Markov Models, IEEE Trans. Automatic Control, under revision, 2007
GERENCSÉR, L. - MICHALETZKY, Gy. - MOLNÁR-SÁSKA, G.: An improved bound for the exponential stability of predictive filters of hidden Markov models, Communications in Information and Systems. Special Volume Dedicated to the 65th Birthday of Tyrone Duncan (guest eds.: A. Bensoussan, S. Mitter and B. Pasik-Duncan), 7.1,, 2007
GERENCSÉR, L. - MÁTYÁS, Z.: A behavioral stock market model, Mathematical Methods of Operations Research, átdolgozás alatt., 2007
CARASSUS, L. – RÁSONYI, M.: Optimal Strategires and Utility-Based Prices Converge When Agents' Preferences Do, Mathematics of Operations Research, vol.32, pp. 102-117, 2007



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