While modern financial networks are so large, complex, and dynamic that the interactions between their members are impossible to model in their entirety, mathematical models with some simplifying assumptions allow for effective study of network dy...
We discuss a new class of applied probability models. There is a system whose evolution is described by a Markov chain with known transition matrix in a discrete state space. At each moment of a discrete time a decision maker can apply one of thre...
This thesis constructs a Defense/Attack resource allocation model. Defender uses "locks" to protect their boxes from Attacker, and Attacker uses "bombs" to destroy as many boxes as possible. The first models of such type were given by E. Borel (19...
We present recursive algorithms to calculate invariant distributions and fundamental matrices of Markov chains specified by the "Islands & Ports'" (IP) model. The state space of the IP model can be partitioned into "islands'" and "ports". An islan...
The purpose of my research is the study of Loop Markov Chains. This model contains several loops, which could be connected at several different points. The focal point of this thesis will be when these loops are connected at one single point. Insi...
