The impact of estimated parameters on optimal decision-making with applications in finance [electronic resource]
Keywords: Management Science and Engineering.

The focus of this dissertation is to investigate the impact of estimated parameters on optimal decision-making. This investigation has two streams. The first stream of this dissertation investigates the optimization bias generated by approximating expectation functions via sample average approximation (SAA). It is a well-known result that using sample average approximation to approximate stochastic programs for which there is not an analytical solution provides an optimal value function which is optimistically biased if the feasibility of approximated solutions can known with certainty. We study the impact of drawing Monte Carlo samples from a simulated distribution with estimated parameters, rather than from the true distribution, on this bias. This is particularly relevant to situations where either (1) the optimal value of the objective function is useful (as a price, for example) or (2) when the optimal value is used as a method of determining the quality of a proposed optimal solution. We consider stochastic programs with expectation constraints and find that under certain circumstances the first order bias can be approximated as the sum of two separately determined biases: the simulation bias due to SAA using true parameter values and the statistical bias of the true problem resulting purely from parameter sensitivity. In addition, we show that when the feasible region must be determined via sampling, the possibility of infeasible approximately optimal solutions potentially reverses the sign of the bias, regardless of whether parameter estimation error is present. This is contrary to the widely used assumption of an optimistic bias. The second stream of this dissertation focuses on the optimization of a collar option strategy, a strategy that is frequently used to improve performance of an investment by protecting one from downside risk at the expense of upside gains. Our analysis optimizes expected utility of single and multi-month strategies where the investor has the three assets available: the risky underlying, put contracts and call contracts with discrete strike prices. For the single month strategies, we find that the investor chooses the collar whose instantaneous replicating portfolio is equal to the optimal mixed strategy calculated using traditional Markowitz optimization without derivative contracts present. We also show that, in the presence of parameter estimation error, regimes exist where collar strategies improve investor performance over a traditional mixed strategy. These simulation results are complimented by an empirical analysis that shows that high performance regimes occur often enough to improve the investor's out of sample certainty equivalent compared to traditional mixed strategies. Existing empirical studies, as well as the empirical work performed within this dissertation, show improved performance with a multi-month strategy over a single month strategy. Our simulation results do not support this result, implying multi-month strategy improved performance cannot be due to the time-value component of derivative contract value as proposed in the existing literature. Instead, we posit multi-month strategy improved performance results from a natural ``hedge'' against either changes in the underlying risky asset's volatility or volatility estimation error.