This paper provides a concise guide to dynamic optimization with an integral treatment on various optimal control and dynamic programming problems. It presents essential theorems and methods for obtaining and characterizing solutions to these problems. The paper discusses Pontryagin's maximum...

The use of American style equity options as hedging instrument has gained currency in recent times. This phenomenon devolves from the ever-expanding need by individuals, corporations and governments to hedge away their financial risks and the clarion call for derivative securities that give the...

Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous-time model. We use the stochastic maximum principle to analyze the model. This method uses forward/backward...

The optimized binomial coefficient or binomial expansion has been derived from the multiple summations of geometric series. This binomial coefficient is a methodological advance in the areas of combinatorics and theoretical computer science. This paper presents a new theorem with binomial...

Index tracking has long been of interest for both industry of fund management andacademia. Various methods have been proposed and tested and various issues arediscussed throughout the past 30 years. Yet one issue remains unresolved is how toperform stock selection optimally. In this paper, I...

The prevalence of electronic devices has propelled the tremendous growth of the semiconductor industry in the past half century. The manufacturing of semiconductor wafers is a long and delicate process, where defect points may occur and cause the failure of the entire circuit. As more advanced...

We introduce the market resources method (MRM) for solving dynamic optimization problems. MRM extends Carroll's (2006) endogenous grid point method (EGM) for problems with more than one control variable using policy function iteration. The MRM algorithm is simple to implement and provides...

We revisit the question whether commodities should be included in investors' portfolios. We employ for the first time a stochastic dominance efficiency (SDE) approach to construct optimal portfolios with and without commodities and we evaluate their comparative performance. SDE circumvents the...

In 1956, Freund introduced the analysis of price risk in a mathematical programming framework. This paper generalizes the treatment of price risk preferences in a mathematical programming framework along the lines suggested by Meyer (1987) who demonstrated the equivalence of expected utility and...