TITLE: Unraveling risks in stochastic models: The “known unknowns” and “unknown unknowns”

ABSTRACT:

Events that model risk are typically characterised by rare occurrences. While designing engineering and financial systems, we want to keep the probability of their failure to be low. This necessitates the study of rare events that represent risk in stochastic models commonly used in operations research and financial engineering. In this talk, we first consider one of the classical models in stochastic operations research, namely, many server queues, and discuss how large delays happen in the presence of heavy-tailed jobs. We shall discuss in depth the two types of effects that dominate the tail asymptotics across various loading regimes. While the quantitative distinction between these two manifests itself only in the slowly varying components in a half-loaded two server queue, we shall see that the two effects arise from qualitatively very different phenomena (arrival of one extremely big job (or) two big jobs). This type of classical large deviation analysis accounts for the type of risk fully represented by the model, commonly referred as “known unknowns”. However, there is an alternate type of risk posed by mis-specifying a model, also referred as “model risk” or “unknown unknowns”. In the second part of the talk, we quickly see how new tools, built on the foundations of mass transportation theory, help us address model risk.

Bio: Karthyek Murthy is a post-doctoral research scientist in the Department of Industrial Engineering & Operations Research at Columbia University. He completed his PhD at Tata Institute of Fundamental Research, Mumbai, where his PhD work on rare events was awarded with best PhD dissertation award for the year 2015. His research interests lie broadly in applied probability & stochastic processes, with special emphasis on models that arise in operations research, insurance and mathematical finance. Building on his PhD work on rare events, he has been recently investigating stochastic modeling techniques that are robust to model risk. His works have been recognized with IBM International PhD fellowship and TCS Research fellowships.