Speaker:  Professor Tomasz Bielecki 

Department of Applied Mathematics,Illinois Institute of Technology

Time:    10:00-11:00AM,Jan 4, 2018

Vanue： 本部览秀楼205

Abstract:   Modelingof evolution of dependence between processes occurring in financial markets isimportant. Typically, one can identify marginal statistical properties ofindividual processes, and then one is confronted with the task of modelingdependence between these individual processes so that the marginal propertiesare obeyed. We have been advocating, for some time now, to address thismodeling problem via the theory of Markov consistency and Markovstructures. 

Inthis talk we shall examine the problem of existence and construction of anon-trivial multivariate Markov chain with components that are given Markovchains. In this regard we shall give sufficient and necessary conditions for acomponent of a multivariate Markov chain to be a Markov chain in the filtrationof the entire chain - a property called strong Markov consistency, as well asin its own filtration - a property called weak Markov consistency. Thesecharacterization results are proved via analysis of the semi-martingalestructure of the chain. 

Severalfinancial applications will be indicated.