| In the first essay, we relate Value at Risk (VaR) to mean-variance analysis and examine the economic implications of using a mean-VaR model for portfolio selection. When comparing two mean-variance efficient portfolios, the higher variance portfolio might have less VaR. Consequently, an efficient portfolio that globally minimizes VaR may not exist. Surprisingly, we show that it is plausible for certain risk-averse agents to end up selecting portfolios with larger standard deviations if they switch from using variance to VaR as a measure of risk. Therefore, regulators should be aware that VaR is not an unqualified improvement over variance as a measure of risk.; In the second essay, we show that multiperiod European options are appropriate derivative securities to generate dynamically complete markets. We find that multiperiod European options on a trading strategy that separates states at the terminal date generate dynamically complete markets. Furthermore, we show that if the uncertainty and information structure in an economy are such that the number of immediate successors of every non-terminal event is non-decreasing over time, then multiperiod European options on a trading strategy generate generically dynamically complete markets under a significantly weaker condition on the trading strategy's terminal dividends. This condition requires the trading strategy to separate states at the terminal date conditional on the information available at the previous date. Finally, we examine the minimum number of options generating generically dynamically complete markets.; In the third essay, we show that American options are appropriate derivative securities to generate complete markets. We begin by examining a two-date economy. We show that if a primitive security separates states, then there exist American options on that security generating complete markets. We then extend this result to a multidate economy. We show that if a primitive security separates states at the terminal date, then generically there exist multiperiod American options on that security generating dynamically complete markets. Finally, we show that there exist economies in which multiperiod American options on a primitive security generate dynamically complete markets even though multiperiod European options on that security cannot generate dynamically complete markets. |
