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CC/GS: Partial Fulfillment of Science Requirement

Prerequisites: STAT GU4203. STAT GU4207 is recommended.

A careful review of the concept of stochastic process as a model of random phenomena evolving through time and of conditional expectation, basic Markov process theory, and the exponential distribution.  Marked point processes and their compensators, beginning with Poisson processes, and proceeding through general marked point processes.  The use of compensators will be justified by the Doob-Meyer decomposition theorem, and as such it will connect the theory to martingales.  Markov processes will enter to provide a description of sufficient conditions for the compensators to have absolutely continuous paths (and as such, have "hazard rates").  Applications to survival analysis and, especially, to mathematical finance, including default and bankruptcy models.  Cox process construction.  This is a core course in the MS program in mathematical finance.