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UID:www.tcs.tifr.res.in/event/1153
DTSTAMP:20230914T125952Z
SUMMARY:An Asymptotic Analysis of Risk in Financial Systems - Analysis and 
 Algorithms
DESCRIPTION:Speaker: Anand Deo\n\nAbstract: \nOver the past few decades\, p
 robabilistic models have become an important tool for under-standing risks
  and decision making in practical financial systems. In the design of suc
 h systems one often wishes to relate the risk to the statistics of underly
 ing stochasticity. However\, this task is complicated by the fact that rea
 listic financial systems are complex\, and undesirable events in them are
  often rare. A large body of research has been devoted to understanding th
 e nature of such rare events\, and how they relate to the stochasticity a
 ffecting the system. In this talk\, we undertake a detailed study of thes
 e aspects in order to develop structural insights on a number of financia
 l systems of practical interest. Our main contributions are as below:\nI. 
 We discuss the development of a closed form\, interpretable parameter esti
 mation technique for predicting defaults of financial firms. Typically\,
  one uses maximum likelihood estimation (MLE) for predicting the firm def
 ault probabilities. We prove that our estimator is almost as accurate as t
 he MLE\, verify our result empirically on a sample of US corporate data\, 
 and showcase the computational/interpretative benefits of our estimator o
 ver the MLE.\nII. We develop a statistically consistent estimator for cond
 itional value-at-risk (CVaR) based optimization objectives and their gradi
 ents. Unlike the state-of-the-art sample average approximations\, the prop
 osed approximation scheme exploits the self-similarity of heavy-tailed dis
 tributions to extrapolate data from lower quantiles\, thereby reducing dat
 a requirements for accurate estimation.\nIII. Motivated by the increasing 
 adoption of models which facilitate automation in risk management and deci
 sion-making\, we present a novel importance sampling (IS) scheme for measu
 ring distribution tails of objectives. Conventional efficient IS approache
 s suffer from feasibility concerns due to the need to intricately tailor 
 the sampler to the underlying probability distribution and the objective. 
 We overcome this challenge in the proposed black-box scheme by automating 
 the selection of an effective IS distribution with a transformation that 
 implicitly learns and replicates the concentration properties observed in 
 less rare samples.\nIV. We develop a limiting representation for an interc
 onnected banking network in presence of partial information. Practical ban
 king networks are large and complicated\, and one searches for simple limi
 ting representations (as the network size goes to infinity). We character
 ise the wealth of banks in a large network in terms of a simple\, one dime
 nsional distributional fixed point\, which we show is amenable to Monte C
 arlo simulation.\nThis talk is based on joint work with Sandeep Juneja and
  Karthyek Murthy.\n\nThe zoom link for the talk is https://zoom.us/j/93128
 173558?pwd=SXRkdFE1MVBnc2hSSEtvbHRIZG4yQT09\n
URL:https://www.tcs.tifr.res.in/web/events/1153
DTSTART;TZID=Asia/Kolkata:20210825T183000
DTEND;TZID=Asia/Kolkata:20210825T193000
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