Modern portfolio theory says that unsystematic risk can always be diversified away. Although it is unrealistic to achieve perfect diversification, people developed different strategies trying to find an optimal portfolio. In this paper, issues of how to make a diversified portfolio are discussed. Six models of tactical portfolio construction strategies are used to make the optimal portfolios using the historical data from Jan. 2007 to Dec. 2009. From the out-of-sample test by market data from Jan. 2010 to Dec. 2011, the classic Markowitz portfolio has the highest wealth added. By comparing the portfolio evaluation parameters, Sharpe ratio suits an individual investor most. And Bayesian portfolio with informative prior scores highest by Sharpe ratio regardless its sensitivity to the accurate market prediction. The paper also demonstrates the application of statistical software R and the "stockPortfolio" package in the stock investment field.

The extent to which the apparent increase in wildfire incidence and burn area in California from 1990 to 2006 is affected by population and temperature increases is examined. Using generalized linear models with random effects, we focus on the estimated impacts of increases in mean daily temperatures and populations in different counties on wildfire in those counties, after essentially controlling for the overall differences between counties in their overall mean temperatures and populations. We find that temperature increase appears to have a significant positive impact on both total burn area and number of observed wildfires. Population growth appears to have a much less pronounced impact on total burn area than do annual temperature increases, and population growth appears to be negatively correlated with the total number of observed wildfires. These effects are especially pronounced in the winter season and in Southern California counties.

The major goal of this thesis is to discuss and test some of the models and fundamental elements of the Modern Portfolio Theory in order to learn about whether the optimal portfolios constructed on the theory formulate the best asset allocation in reality. In an effort to solve this question, three different models are tested by three fundamental elements of the theory respectively. The outcomes for each model and element are discussed and evaluated.

The empirical result shows that the models are inconsistent, which leads to the conclusion that optimal portfolios based on Modern Portfolio Theory are not the best asset allocation strategies in the real investment world. The main reason can be concluded that the models based on the theory make oversimplified approximations of the reality.

Hepatocellular carcinoma is the sixth most common cancer worldwide and the leading cause of death among patients with cirrhosis. The vast majority of these patients have the unresectable, intermediate-stage form of the disease, for which the standard of care is transarterial chemoembolization. With the health care sector rapidly outgrowing the national economy, maximizing value is now a major priority in health policy, especially with regard to cancer. Recent evidence suggests that stereotactic body radiotherapy may be a viable alternative to transarterial chemoembolization among patients of in early or very early stage of carcinoma. This evidence warrants a cost-effectiveness analysis, which not been conducted to date; the results of this study may directly impact practice guidelines for this disease. A Markov decision model was used to model the clinical trajectory of a typical patient with unresectable hepatocellular carcinoma. Costs were derived from a combination of previous studies and economic outcomes data. We hypothesized that stereotactic body radiotherapy achieves significantly greater cost-effectiveness than the current standard of care for hepatocellular carcinoma but we found the opposite may be in fact true and that transarterial chemoembolization may a more efficient management strategy for typical patients with unresectable hepatocellular carcinoma.

An algorithm is devised for clustering observations based on the densities of points within each individual observations. The Kernel Density Estimation Clustering Algorithm (KCA) performs a search on the graph of the observations' group memberships, where group memberships determines the KDEs that in turn drive changes in the objective function. Option pricing theory is used to demonstrate the utility of the algorithm. Volatility smiles, 2- dimensional plots relating option strike prices and their implied volatilities, are the basis for grouping options.