Jeffrey Collamore's inaugural lecture

Jeffrey Collamore will hold his inaugural lecture from 14:00-14:45. At 15:00 everyone is invited to a reception in the lunchroom on the 4th floor (04.4.19 + 20).

Jeffrey Collamore afholder sin tiltrædelsesforelæsning den 1. marts 2019 i Auditorium 4 kl. 14:00-14:45. Kl. 15:00 inviteres alle til reception i frokoststuen på 4. sal (04.4.19+20).

Title:
Risk theory, large deviations, and the study of stochastic recursive sequences

Abstract:
Starting with the work of H. Cramér in the 1930s, the theory of large deviations has played a prominent role in pure and applied probability. We will briefly review the history, starting with the “ruin problem” in non-life insurance, and turning to some of its more modern extensions in the work of Varadhan. Next, we will relate this work to the study of stochastic recursive sequences. Such sequences have been of contemporary interest in many areas, including financial time series modeling, integrated financial-insurance risk models, the study of branching processes, among other areas. We present some recent and ongoing work (joint with A. Vidyashankar, S. Mentemeier, and E. Damek et al) characterizing the path properties of stochastic recursive sequences, and describing, in particular, the “likely” time or path to a rare event in the sense of large deviation theory. We conclude by outlining a few future directions.