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UID:www.tcs.tifr.res.in/event/1079
DTSTAMP:20230914T125949Z
SUMMARY:An Asymptotic Study of Financial Systems - Algorithms and Analysis
DESCRIPTION:Speaker: Anand Deo\n\nAbstract: \nOver the past few decades\, a
symptotic study of financial systems has become an integral part of practi
cal decision making and analytics. Realistic financial systems are complex
\, and undesirable events in them are often rare. In order to gain more in
sights into their behaviour\, it is important to develop structural simpli
fications and efficient computational algorithms for rare event analysis.
In this talk\, we undertake a detailed study of these aspects\, and develo
p structural insights on a number of financial systems of practical intere
st.\n\nIn the first part\, we consider two problems related to rare event
analysis:\n\n1) The estimation of default probabilities of financial firms
from data is an important problem which has received significant attentio
n over the past two decades. We discuss the development of a closed form\,
interpretable parameter estimation technique for predicting defaults of f
inancial firms. Typically\, one uses Maximum Likelihood Estimation (MLE) f
or predicting the firm default probabilities. We prove that our estimator
is almost as accurate as the MLE for a realistic sample of financial data.
Further since our estimator is closed form\, it is significantly faster t
han MLE. Finally\, we demonstrate that unlike the MLE our estimator also g
ives interesting structural insights - specifically\, we show that from th
e standpoint of default prediction\, collecting covariate data just before
occurrence of default is sufficient to estimate probabilities.\n\n2) Buil
ding upon the well established notions of multivariate regular variation a
nd large deviations theory\, we derive a unified framework\, in which tail
analysis of a large class of stochastic loss functions can be performed.
Within this framework\, assuming the underlying stochasticity is heavy tai
led\, we develop a data-driven estimator for tail exceedences of a large c
lass of financial losses\, and applying it to a tail risk-constrained port
folio optimisation problem\, showcase superior performance over the state
of the art. Additionally\, assuming oracle access to the densities of loss
causing covariates\, we develop a self-replicating\, provably accurate im
portance sampling algorithm to estimate rare event probabilities over a va
riety of covariate/loss structures.\n\nIn the latter part of the talk\, we
develop a limiting representation for an interconnected banking network i
n presence of partial information. Practical banking networks are large an
d complicated\, and one searches for simple limiting representations (as
the network size goes to infinity). We characterise the wealths of banks i
n a large network in terms of a simple\, one dimensional distributional fi
xed point\, which we show is amenable to simulation. While such fixed poin
t representations have been well studied when the network is of a finite s
ize\, to the best of our knowledge\, our work is the first to provide a si
mplified limiting representation.\n
URL:https://www.tcs.tifr.res.in/web/events/1079
DTSTART;TZID=Asia/Kolkata:20200827T103000
DTEND;TZID=Asia/Kolkata:20200827T113000
LOCATION:Zoom link for meeting. https://zoom.us/j/97134023137?pwd=b
XJwTkFHNFQxcDkyR2JaMkVaTk5WQT09
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