“Some Advances in Modeling, Optimization and Control of Stochastic Dynamics -- Applications in Finance, Economics, Biology and Environment”





Gerhard-Wilhelm Weber

(Institute of Applied Mathematics -- METU)



Abstract: This presentation introduces into some recent research achievements in continuous-time models of the financial sector and related fields, supported by mathematics. Stochastic Optimal Control has an increasingly important role in science, economics and the sectors of environment and finance, and is extensively used in various applications. We present applications of Stochastic Hybrid models in biology, ecology, monetary systems and finance to account for regime switching dynamics. Stochastic models with a motion part and additionally a jump part are able to capture abrupt fluctuations that are a usual phenomenon in genetic and environmental networks and in financial markets. These kinds of models allow for more realistic investigation of portfolio optimization and utility maximization in financial markets and in genetic, metabolic and ecological interaction. The models comprise portfolio optimization with optimal investment and consumption strategies. Explicit consideration of risk aversion in an optimal investment and consumption problem allows for optimality conditions that are related to specific risk types in a market. A more general model for portfolio and gene-environment optimization is established afterwards. In another study, we develop a new theory of estimating Hurst parameter using conic multivariate adaptive regression splines (CMARS) method. Stochastic Differential Equations (SDEs) generated by fractional Brownian motion (fBm) with Hurst parameter, H, are widely used to represent noisy and real-world problems. The reason why fBm is preferred in modelling, to other Markov processes is its property of capturing the dependence structure of observations. It is, therefore, a more realistic model compared to Markov processes. The superiority of our approach to the others is, it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated test data. The presentation ends with a conclusion and an outlook to future studies.



Date : March 27, 2013 (Wednesday)

Time : 15.40-16.30

Place: Bilkent University ,Mathematics Seminar Room SA141 Tea and cookies will be served after the seminar.