Laboratory for Qquantitative Finance

• Our researchers have proposed a general scheme for dual characterization of the cost function in the problem of maximization of utility of terminal capitalization. Depending on the type of the utility function we have reviewed two different definitions of the problem in which we managed to rid of singular functionals which allowed to achieve significant progress in comparison with earlier research.
• We have produced a characterization of minimax testing in problems of checking two complex hypotheses in application to the problem of efficient partial hedging of European in incomplete markets.
• The Laboratory has studied the problem of dynamics of stock markets of developing countries, including Russia.
• We have investigated the problem of building hedging strategies in the light of expenses for financial markets with random volatilities.
• New results have been achieved in the problem of detecting discords of random processes with applications to questions of choice of trading strategies.
• We have produced distributions of functionals of the «maximum type» on intervals containing excursions of reviewed discrete and continuous random processes.
• The Laboratory has obtained new data of models of probability of default of Russian banks in logistical specifications with quasi panel data structure (1998–2011).
• We have proposed a methodology and developed a model for assessing probability for project funding deals within internal ratings-based approach (IRB Approach) using economic models of binary choice.
• An algorithm has been created for making decisions on participation in implementation of investment projects for project financing deals in Russia.
• Methods and models have been developed for assessment of credit risks that factor in peculiarities of the Russian mortgage market. The models will be used by credit organizations in their in their internal risk management systems.
• Our research has proven that for a model of a financial market for which the requirement of absence of asymptotic arbitrage of the first kind is satisfied, in any proximity of the initial probability measure there is an equivalent probability measure that allows for a local Martingale deflator that is inverse to the process of cost of some portfolio.
• We have investigated the problem of optimal investing in the Heston stochastic volatility model. Unknown decisive formulas have been produced that describe the optimal investment strategy for assets whose dynamics complies with the Heston stochastic volatility model. We have produced formulas that had not been known before that describe investing in assets whose dynamics comply with the Linetsky-Carr local volatility model.
• The Laboratory has studied the problem of cointegration of macroindicators and financial indicators of the economics of the Russian Federation (GDP, M2 monetary aggregate and real exchange rate) and worldwide oil prices. We have found that cointegration can be educed with sufficient reliability only between oil prices and GDP.
• Our research has shown that long-term correlation between economic indicators is maintained exactly by presence of oil prices in the model and their significant impact on the system as a whole.
• We have proposed and analyzed new models of financial bubbles, system risk, defaults of banks and insurance companies investing their reserves into high-risk assets. 

Education and career development: In 2013-2014 we have conducted 3 international conferences and a summer school in financial mathematics.

Collaborations: P. N. Lebedev Institute of Mathematics o the Russian Academy of Sciences (Russia), University of Rouen (France), University of Paris 7 (France), Paris Dauphine University (France), University of Franche-Comté (France), University of Zurich (Switzerland), Carnegie Mellon University (USA): collaborative work