The project "Innovative Models for Pricing and Reselling of Options" was realised at Mälardalen University (School of Education, Culture and Communication). The project was realised in the period 2009.01.01 – 2013.12.31, which also included one year extension period granted by the Riksbankens Jubileumsfond.
The project has been carried out by the research group led by Professor Dmitrii Silvestrov (Stockholm University and Mälardalen University). The research group has been also including at different stages, Professor A. Malyarenko, Dr. E. Silvestrova, Dr. H. Jönsson, Dr. F. Stenberg, Dr. R. Lundgren, postdoctoral fellow V. Masol (all, Mälardalen University), Professors A. Kukush (Kiev University), Professor R. Manca (University of Rome "La Sapienza").
The research program of the project is complete. New research results on convergence and skeleton approximations for rewards of American type options for multivariate modulated Markov log-price processes including modulated Lévy and autoregressive log-price processes, Markov Gaussian log-price processes, reselling of options, multi-threshold structure of optimal stopping domains and new types of Monte Carlo based algorithms for option pricing, new approximation results for reselling of European options and American knock out options and new backward algorithms for accumulated Markov and semi-Markov rewards have been obtained.
The results obtained in the project generated a new prospective directions for research on stochastic approximation methods for option type and forward contracts in financial mathematics.
The main elements of the implementation plan for the RJ project have been: to write a book on American type options for modulated price processes; to prepare and to publish a number of research papers (more than 15); to report the results of the project at the international conferences and workshops (more than 10), to complete and to defend one PhD Thesis in the research area of the project; to realize a number of master projects in the area of the project. This plan has been carried out.
The book, Silvestrov, D.S. American-Type Options. Stochastic Approximation Methods. Volume I. De Gruyter Studies in Mathematics, 56, De Gruyter, 2013, X + 510 pages, have been published.
The results of the project have also been published in 23 research papers and reported at 17 international conferences and workshops, including 9 plenary invited lectures given by the project leader, and have got a good response among the researchers and experts in the area of financial mathematics. Professor Silvestrov also took part in organization of 10 international conferences and workshops, where results of the project have been presented. Robin Lundgren (supervised by Professor D. Silvestrov) defended PhD dissertation "Convergence of Option Rewards in 2010 (Mälardalen University).
The book mentioned above is the 1st part of a comprehensive two-parts monograph. The theoretical and experimental research studies connected with the 2nd volume of the book have been completed during the project extension period according the plan proposed for this period. At present, the 2nd volume is at stage of preparation. It is planned to be submitted and published in 2014.
There exist an open access to all publications representing results of the project. They are also listed in CV of the project leader.
Positive results of the RJ project presented above let me conclude that the RJ Project "Innovative Models for Pricing and Reselling of Options" is successfully completed and its results are effectively implemented at national and international levels.