20 research outputs found
Signal Processing under Active Monitoring
This paper describes a method of signal preprocessing under active monitoring. Suppose we want to
solve the inverse problem of getting the response of a medium to one powerful signal, which is equivalent to
obtaining the transmission function of the medium, but do not have an opportunity to conduct such an experiment
(it might be too expensive or harmful for the environment). Practically the problem can be reduced to obtaining
the transmission function of the medium. In this case we can conduct a series of experiments of relatively low
power and superpose the response signals. However, this method is conjugated with considerable loss of
information (especially in the high frequency domain) due to fluctuations of the phase, the frequency and the
starting time of each individual experiment. The preprocessing technique presented in this paper allows us to
substantially restore the response of the medium and consequently to find a better estimate for the transmission
function. This technique is based on expanding the initial signal into the system of orthogonal functions
An expansion in the model space in the context of utility maximization
In the framework of an incomplete financial market where the stock price
dynamics are modeled by a continuous semimartingale (not necessarily Markovian)
an explicit second-order expansion formula for the power investor's value
function - seen as a function of the underlying market price of risk process -
is provided. This allows us to provide first-order approximations of the
optimal primal and dual controls. Two specific calibrated numerical examples
illustrating the accuracy of the method are also given