Seminar on Computer Science and Applied Mathematics

PROGRAM

Utorak, 12.07.2016. u 14:00, soba 301f, MI SANU:
Srdjan Stojanovic, Department of Mathematical Sciences, University of Cincinnati, Ohio, USA
FINANCIAL MATHEMATICS FOR INCOMPLETE MARKETS: GENERAL THEORY, COMPUTER IMPLEMENTATIONS, AND APPLICATIONS
Abstract: The classical financial mathematics, due to Black, Scholes, and Merton, was developed for the so-called complete markets, i.e., markets where (theoretically) it is possible to hedge all the market risk of holding a position in a financial asset, by means of continuous trading in another perfectly correlated tradable. If no perfectly correlated tradable exists, market is said to be incomplete. In such a setting, since risk cannot be completely eliminated, it must be priced, i.e., one has to compute the risk-premium. To that end two well respected pricing paradigms, indifference and neutral pricing, were introduced, in a relatively simple settings, by various authors.
Theory of neutral (i.e., optimal) and indifference pricing, hedging, and optimal trading for portfolios of financial contracts, for completely general diffusive Markovian continuous-time financial models is nowadays available, due to the works of the speaker (as elaborated in his book "Neutral and Indifference Portfolio Pricing, Hedging and Investing", Springer, New York, 2012). Furthermore, this general theory is fully implemented using symbolic calculations on Mathematica computer platform: from SDE underlying models, via pricing and optimal portfolio PDEs and ODEs, to their symbolic and/or numerical solutions. As a consequence, financial engineering solutions of unprecedented complexity can be achieved in both, complete and incomplete markets. This talk will give an overview of the general theory, and showcase the above claims on some applications in interest rates, commodities, and commodity derivatives.