Systems engineering of the financial-investment informatization projects and the prognosis enterprise bankruptcy risks
The unified model of portfolio investment system consists of a structural, dynamic, use case and calibration representations. The system provides desired features: efficiency, scalability, extensibility, reliability, safety, transparency and low total cost of ownership.
The following mathematical models and method in the financial engineering are introduced: portfolio optimization model, derivatives pricing model and risk estimation method — nonparametric Monte Carlo. The portfolio optimization model allows for the change of returns' distribution over time. The model does not require apriori assumptions about the shape of the returns' statistical distribution. The derivatives pricing model (the stochastic mean multifractal volatility model) improves the accuracy of the derivative's price estimation by modeling volatility with the multifractal random process. The method for dependent random variables modelling for risk estimation, nonparametric Monte Carlo, doesn't require the compulsory choice of random variables distributions prior to simulation. Nonparametric Monte Carlo combines the advantages of the historical simulation and conventional Monte Carlo. The risk underestimation problem of Monte Carlo method caused by normal distribution assumption is overcome.
New models and methods for analysis of the enterprise’s financial state and prognosis of the bankruptcy under conditions of incompleteness and indeterminacy of the information have been introduced. These methods and models are based on the fuzzy logic and fuzzy neural networks. A complex of programs has been created that implement proposed methods and algorithms.
The results of the research are used in the academic activity in the courses “Fuzzy models and methods in the intellectual systems”. 3 PhD theses, 5 master theses and 6 diploma theses have been defended, 1 monograph and 15 articles have been published. The results have been discussed on 10 conferences. 12 students were involved in the research.
The results of the research were used in the “Potential Credit Exposure” project of the swiss bank UBS AG.