will speak on
Stochastic differential equations (SDEs) are commonly used in
modeling the trajectories of processes whose motion is determined by
random movements. In particular, we are interested in the application of
SDEs to
inefficient financial markets (IFM) in which investors take historical information
into account when making their investment decisions. We study
the almost sure asymptotic rate of growth of the partial maxima and
minima of solutions of both linear and non-linear SDEs, as these represent
the
largest possible fluctuations in the price or returns of the asset.
Since in IFM, prices or returns exhibit short run positive
autocorrelations (which mimic market bubbles), SDEs involving delay factors
are
investigated and compared with SDEs under the classical Efficient
Market Hypothesis. We also develop Markov models driven by
semi-martingales other than standard Brownian motion. While these
semi-martingales preserve the size of large fluctuations of Brownian
markets, they differ from Brownian motion by possessing
dependent increments, and so can create the presence of non-trivial
autocorrelations in security returns.
The work is joint with my supervisor Dr. John Appleby.
(This talk is part of the IMS September Meeting 2007 series.)