“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.