In this dissertation we employ two different optimization methodologies, dynamic

programming and linear programming, and stochastic simulation. The first

two essays are drawn from military manpower modeling and the last is an application

in finance.

First, we investigate two different models to explore the military manpower

system. The first model describes the optimal retirement behavior for an Army

officer from any point in their career. We address the optimal retirement policies for

Army officers, incorporating the current retirement system, pay tables, and Army

promotion opportunities. We find that the optimal policy for taste-neutral Lieutenant

Colonels is to retire at 20 years. We demonstrate the value and importance

of promotion signals regarding the promotion distribution to Colonel. Signaling an

increased promotion opportunity from 50% to 75% for the most competitive officers

switches their optimal policy at twenty years to continuing to serve and competing

for promotion to Colonel.

The second essay explores the attainability and sustainability of Army force profiles. We propose a new network structure that incorporates both rank and

years in grade to combine cohort, rank, and specialty modeling without falling into

the common pitfalls of small cell size and uncontrollable end effects. This is the

first implementation of specialty modeling in a manpower model for U.S. Army

officers. Previous specialty models of the U.S. Army manpower system have isolated

accession planning for Second Lieutenants and the Career Field Designation

process for Majors, but this is the first integration of rank and specialty modeling

over the entire officer's career and development of an optimal force profile.

The last application is drawn from financial engineering and explores several

exotic derivatives that are collectively known Mountain Range options, employing

Monte Carlo simulation to price these options and developing gradient estimates

to study the sensitivities to underlying parameters, known as "the Greeks". We

find that IPA and LR/SF methods are efficient methods of gradient estimation for

Mountain Range products at a considerably reduced computation cost compared

with the commonly used finite difference methods.