Abstract: This paper studies the optimal investment strategies for a plan member (PM) in a defined contribution (DC) pension scheme with transaction cost, taxes on invested funds and couple risky assets (stocks) under the Ornstein-Uhlenbeck (O-U) process. The PM’s portfolio is assumed to consist of a risk-free asset and two risky assets where the two risky assets are driven by the O-U process. The Legendre transformation and dual theory is use to transform the resultant optimal control problem which is a nonlinear partial differential equation (PDE) into linear PDE and the resultant linear PDE is then solved for the explicit solutions of the optimal investment strategies for PM exhibiting constant absolute risk aversion (CARA) using change of variable technique. Furthermore, theoretical analysis is used to study the influences of some sensitive parameters on the optimal investment strategies with observations that the optimal investment strategies for the two risky assets increase with increase in the dividend and decreases with increase in tax on the invested funds, risk averse coefficient, initial fund size and the transaction cost.
Abstract: Ultrasound (US) is widely used in medical field for
a variety diagnostic techniques but, in recent years, it has also
been creating great interest for therapeutic aims. Regarding drug
delivery, the use of US as an activation source provides better
spatial delivery confinement and limits the undesired side effects.
However, at present there is no complete characterization
at a fundamental level of the different signals produced by
sono-activated nanocarriers. Therefore, the aim of this study
is to obtain a metrological characterization of the cavitation
phenomena induced by US through three parallel investigation
approaches. US was focused into a channel of a customized
phantom in which a solution with oxygen-loaded nanodroplets
(OLNDs) was led to flow and the cavitation activity was
monitored. Both quantitative and qualitative real-time analysis
were performed giving information about the dynamics of
bubble formation, oscillation and final implosion with respect
to the working acoustic pressure and the type of nanodroplets,
compared with pure water. From this analysis a possible
interpretation of the observed results is proposed.