Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

Dr. Ricardas Zitikis

2nd Supervisor

Dr. Jiandong Ren

Joint Supervisor

Abstract

Everyday, we make difficult choices under uncertainties. The decision making process becomes even more complicated when more agents get involved: one must consider their interactions and conflicts of interest because the final outcome is based not only on an agent's decision but on everybody's.

In insurance industry, companies try to avoid making large claim payments to policyholders (commonly known as insureds) by purchasing reinsurance policies from reinsurance companies (the reinsurer). Each policy details conditions upon which the reinsurer pays a share of the claim to the insurance company (also known as the cedent or the insurer). To reach an agreement, the interests of both parties must be taken into consideration. In this thesis, we will discuss approaches for constructing optimal reinsurance policies that are beneficial to both the insurer and the reinsurer.

Likewise, we have similar situations in real estate industry, where sellers and buyers negotiate contracts. For example, the difference between the seller's selling price and the buyer's budget (commonly referred to as the buyer's reservation price) affects the intensity of buyer arrivals, the bargaining process and its rate of success, as well as many other parameters. We will explore the likelihood of the buyer purchasing a property given factors such as the buyer's reservation price and the negotiated selling prices, which may or may not be dependent random variables.

Of course, these are just two illustrative scenarios that make our results more intuitive and better appreciated from the practical point of view, which has been a very important consideration throughout the thesis. Furthermore, it will be easily seen when reading the thesis that our developed and discussed methodologies can be adapted to numerous other scenarios, which may in turn require making certain adjustments to our results. Nevertheless, we are confident that the herein developed considerations are very general in nature and can already be used to facilitate decision making.

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