Optimal execution of real-options in illiquid and incomplete markets

This dissertation, consists of three essays on the problem of quantifying optimal stopping policies for a multi-period investment, where transition probabilities and the investment value itself are uncertain. These models are applicable to entrepreneurs in the technology sector and any investment where option based approach can be taken. In the first chapter, I convert the multi-period investment into a partially observable Markov decision process model with bayesian learning. I assume that the core process of the investment value is not observable during the multi-period investment process but can be observed only in its final state if the decision to exploit the investment is made. I assume that the probability distribution between the observed demand levels and the underlying value is known. Since this POMDP model is difficult to solve with dynamic programming because of the size of the possible states, we introduce a heuristic based on marginal profit gains at each state. With the marginal profit heuristic we can calculate the minimum probability threshold of the unobservable state, in a 2-state model, that is the optimal stopping for the process. In the second chapter, I drop the assumption of knowing the probability distribution between the observable demand and unobservable underlying value of the state to the investment, and replace it with a second type of demand level that when observed together with the first demand level imply certain values of the underlying investment. I introduce an algebraic logistic function that has the characteristics of a sigmoid distribution, to serve as an approximation of the probability of the underlying state, based on the observations of the two demand levels but the ratio between them quantify the probability, not a known distribution. Since this model has no defined transition matrix, I develop a best case heuristic, for the 2-state model, that finds a local optimal range, without the use of the Lambert function, and therefore optimal stopping point when a local optimal range does not exist. For the n-state model we define least-case heuristic, similar to the best-case heuristic, except m-local optimal ranges are defined, where m