Pension Plan Member’s Investment Strategies with Transaction Cost and Couple Risky Assets Modelled by the O-U Process

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.

Multiple Approaches for Ultrasonic Cavitation Monitoring of Oxygen-Loaded Nanodroplets

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.