5,805 research outputs found
Optimal long term investment model with memory
We consider a financial market model driven by an R^n-valued Gaussian process
with stationary increments which is different from Brownian motion. This
driving noise process consists of independent components, and each
component has memory described by two parameters. For this market model, we
explicitly solve optimal investment problems. These include (i) Merton's
portfolio optimization problem; (ii) the maximization of growth rate of
expected utility of wealth over the infinite horizon; (iii) the maximization of
the large deviation probability that the wealth grows at a higher rate than a
given benchmark. The estimation of paremeters is also considered.Comment: 25 pages, 3 figures. To appear in Applied Mathematics and
Optimizatio
Linear filtering of systems with memory
We study the linear filtering problem for systems driven by continuous
Gaussian processes with memory described by two parameters. The driving
processes have the virtue that they possess stationary increments and simple
semimartingale representations simultaneously. It allows for straightforward
parameter estimations. After giving the semimartingale representations of the
processes by innovation theory, we derive Kalman-Bucy-type filtering equations
for the systems. We apply the result to the optimal portfolio problem for an
investor with partial observations. We illustrate the tractability of the
filtering algorithm by numerical implementations.Comment: Full names are use
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