Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Ali Kassir
Thursday, May 31, 2018
4:00 pm - 4:50 pm
RH 440R

Talk Abstract:

In this presentation, we explore Markov chains with random transition matrices. Such chains are a development on classic Markov chains where the transition matrix is taken to be random. The intuition for this is that we may be interested in modeling phenomenas where the homogeneity assumption of classic Markov chains is invalid. We first use such chains to model credit risk. The randomness of the transition matrix is used to represent the randomness of the economy that underlies credit risk. With this, we model a portfolio of loans and the risk due to having a shared economy. We then proceed to explore theoretical properties of such chains with a focus on their asymptotic behavior. In the case of absorbing chains, we show that the the infinite product of independent and identically distributed random matrices must converge almost surely. We also introduce perturbed Markov chains as a special form of Markov chains with random transition matrices and look at some applications.

About the Speaker:

Ali has been a student for 9 years at UCI and is glad to graduate. He is currently working as a data scientist at iHerb Inc. He is the father of two beautiful children. His wife has only known him as a graduate student and is excited to discover her non-graduate student husband.

Refreshments:

Pizza will be served after the talk.