Continuous-Time Markowitz's Model with Transaction Costs

A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon. With a series of transformations, the problem is turned into a so-called double obstacle problem, a well studied problem in physics and partial differential equation literature, featuring two time-varying free boundaries. The two boundaries, which define the buy, sell, and no-trade regions, are proved to be smooth in time. This in turn characterizes the optimal strategy, via a Skorokhod problem, as one that tries to keep a certain adjusted bond-stock position within the no-trade region. Several features of the optimal strategy are revealed that are remarkably different from its no-transaction-cost counterpart. It is shown that there exists a critical length in time, which is dependent on the stock excess return as well as the transaction fees but independent of the investment target and the stock volatility, so that an expected terminal return may not be achievable if the planning horizon is shorter than that critical length (while in the absence of transaction costs any expected return can be reached in an arbitrary period of time). It is further demonstrated that anyone following the optimal strategy should not buy the stock beyond the point when the time to maturity is shorter than the aforementioned critical length. Moreover, the investor would be less likely to buy the stock and more likely to sell the stock when the maturity date is getting closer. These features, while consistent with the widely accepted investment wisdom, suggest that the planning horizon is an integral part of the investment opportunities.Comment: 30 pages, 1 figur

Microstructure Control and Performance Evolution of Aluminum Alloy 7075 by Nano-Treating.

Nano-treating is a novel concept wherein a low percentage of nanoparticles is used for microstructural control and property tuning in metals and alloys. The nano-treating of AA7075 was investigated to control its microstructure and improve its structural stability for high performance. After treatment with TiC nanoparticles, the grains were significantly refined from coarse dendrites of hundreds of micrometers to fine equiaxial ones smaller than 20 μm. After T6 heat treatment, the grains, with an average size of 18.5 μm, remained almost unchanged, demonstrating an excellent thermal stability. It was found that besides of growth restriction factor by pinning behavior on grain boundries, TiC nanoparticles served as both an effective nucleation agent for primary grains and an effective secondary phase modifier in AA7075. Furthermore, the mechanical properties of nano-treated AA7075 were improved over those of the pure alloy. Thus, nano-treating provides a new method to enhance the performance of aluminum alloys for numerous applications

Coordination States and Catalytic Performance of Ti in Titanium Silicalite-1

In the past two decades, we studied the synthesis, modification, and application of titanium silicalite-1 (TS-1) systematically with the goal of exploring its role as a catalyst for industrial selective oxidation reactions. Three factors were primarily considered for catalytic performance: the coordination states of titanium ions, locations of titanium ions, and diffusion properties. The coordination state of Ti, which was the most important of all the three factors, was tuned by controlling the synthesis conditions and posttreating with organic bases. Spectroscopy was used to help establishing the relationship between catalytic activity and coordination state. More active titanium species were located on the external surface by posttreatment, so the catalytic performance for larger molecules was improved significantly. The diffusion properties can be enhanced by posttreatment with organic bases. Furthermore, meso−/microporous titanium silicalite was synthesized by one-pot synthesis with cetyltrimethyl ammonium bromide (CTAB) as a mesoporous porogen. The TS-1 plate with a short b-axis length was also provided