Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Statistics and Actuarial Sciences


Ricardas Zitikis


Motivated by some real problems, our thesis puts forward two general two-period pricing models and explore optimal buying and selling strategies in two states of the two-period decision, when buyer/seller's decisions in the two periods are uncertain: commodity valuations may or may not be independent, may or may not follow the same distribution, be heavily or just lightly influenced by exogenous economic conditions, and so on. For both the example of buying laptops and the example of selling houses, the connections between each example and the two-envelope paradox encourage us to explore optimal strategies based on the works of McDonnell and Abbott (2009) and McDonnell et al. (2011), which proposed optimal strategies on the condition that the amount of the first envelope is known. In the case of buying laptop whether on Black Friday, or on Boxing day, We derive an optimal strategy for minimizing the expected loss in the two-period economy when a pivotal decision needs to be made during the first time-period and cannot be subsequently reversed. In the cases of selling real estate in Punta del Este, a resort town in Uruguay, real-estate property is in demand by both domestic and foreign buyers. There are several stages of selling residential units: before, during, and after the actual construction. Different pricing strategies are used at every stage. We propose a general model to derive, under various scenarios of practical relevance, optimal strategies for setting prices within two-stage selling framework, as well as to explore the optimal timing for accomplishing these tasks in order to maximize the overall seller's expected revenue. The optimal strategies in this model draw hints from the example of selling real estate proposed by Egozcue et al. (2013), where the ideas of McDonnell and Abbott (2009) and McDonnell et al. (2011) were applied in two states of the one-period decision scenario. All our optimal buying/selling strategies are illustrated with numerical and graphical examples using appropriately constructed parametric models.