This application of gradient estimation drawn from financial engineering and ex- plores several exotic derivatives that are collectively known Mountain Range options, employing Monte Carlo simulation to price these options and developing gradient es- timates to study the sensitivities to...

Stop-Loss is an Army policy which requires Soldiers to remain in the Army beyond their contractual obligation in order to complete a unit's deployment to Iraq or Afghanistan. Stop-Loss was implemented to maintain unit cohesion and stabilize the force. We address projecting the quantity of...

At the heart of any decision problem is some degree of "flexibility" in how to act. Most often, we aim to extract greatest possible value from this inherent flexibility. The three essays compiled here are aligned with this same general aim, but we have an important secondary concern: to...

We study sensitivity analysis of portfolio credit derivatives, including basket default swaps and collateralized debt obligations. An unbiased estimator is derived using conditional Monte Carlo for sensitivities with respect to systemic parameters (parameters that influence some or all the...

We consider estimating an expected infinite-horizon cumulative cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the...

The generalized likelihood ratio (GLR) method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances. We put the GLR methods from previous work into a single framework, simplify regularity conditions to justify the unbiasedness of...

The Expectation-Maximization (EM) algorithm is a very popular optimization tool for mixture problems and in particular for model-based clustering problems. However, while the algorithm is convenient to implement and numerically very stable, it only produces local solutions. Thus, it may not...