Dr. Anindya Goswami
Office: A404 Main Building
IISER Campus
Dr. Homi
Bhabha Road, Pashan
Pune 411008, India
Phone: +91 (20) 2590 8105
anindya(a)iiserpune.
ac. in
Research
interest:
·
Mathematical Finance,
Stochastic Processes and Control
Publication:
·
A
complete list by Google
Scholar Citation
·
Other
online database by MathSciNet,
ORCID, Research
Gate, Scopus, ZbMATH
Other
links:
·
Teaching
Notice:
·
Postdoctoral
position (Apply before 10^{th} August)
Advt.
No.43/2017 in http://www.iiserpune.ac.in/links/jobopportunities
·
Statistical
Methods in Finance 2018
Events:
·
Workshop on
Mathematical Finance 2018
·
Inter
IISER Mathematics Meet (IIMM) 2017
About
me: I received my Bachelor's degree
in Mathematics from St. Xavier's College, Calcutta in 2002. Later in the same
year, I joined the Integrated Ph.D. program in the Department of Mathematics
in Indian Institute of Science, Bangalore. Following the completion of my MS
degree in 2005, I received the SPM fellowship as part of the National Award
for best performance in National Eligibility Test in Mathematical Sciences.
My MS thesis was titled “Controlled SemiMarkov Processes with Partial
Observation”. I was bestowed with the Doctorate degree from the
Department of Mathematics, IISc in the year 2008.
(Link to my Ph.D thesis“SemiMarkov
Processes in Dynamic Games and Finance”) The following three years,
I carried out my postdoctoral research in the University of Twente, Netherlands; INRIA Rennes, France; and Technion Israel Institute of Technology, Israel
respectively. I joined IISER Pune as an Assistant Professor in fall, 2011.
Since then, I have offered a variety of graduate and undergraduate courses
Multivariable Calculus, Pointset Topology, Measure Theory, Functional
Analysis, Numerical Analysis, Stochastic Processes, Mathematical Finance, to
name a few. I am reappointed at the same department as an Associate Professor
in spring, 2018. My current research interest comprises of Noncooperative
Stochastic Dynamic Game, Stochastic Control, Mathematical Finance, and
Queueing Network. So far, I have coauthored many peerreviewed research
articles published in wellreputed journals including J. Math. Anal. Appl.,
SIAM J. Control Optim., Appl. Math. Optim., Electron. Commun. Probab., Statist. Probab. Lett.
and Stoch. Anal. Appl. I am an invited reviewer of
Mathematical Reviews, published by American Mathematical Society and I also
regularly take up refereeing responsibility from several Mathematics journals
and book publishers. Research
Summary on Derivative Pricing: One of my research goals is to
broaden the existing theory of option pricing to include some of the stylized
facts in the asset price model, such as long memory effect, stochastic
volatility, heavytail distribution of log return, jump discontinuities of
asset price etc. In the classical model of stock prices by
BlackScholesMerton(BSM), which is assumed to be Geometric Brownian Motion,
the drift and the volatility of the prices are held constant. However, in
reality, the empirical volatility varies over time. In regime switching
model, it is assumed that the market has finitely many hypothetical
observable economic states and those are realized for certain random
intervals of time. In particular, the volatility is assumed to depend on
those regimes or states and the state transitions are modeled by a pure jump
process. The Market model with finitestate Markov regime is a very popular
choice. In comparison with Markov
switching, the study of semiMarkov (SM) regime switching is relatively
uncommon. In this type of models, one has an opportunity to incorporate some
memory effect of the market. In particular, the knowledge of past stagnancy
period can be fed into the option price formula to obtain the price value.
Hence this type of models has greater appeal in terms of applicability than
the one with Markov switching. The pricing problem with SM
regimes was first correctly solved in a paper with Mrinal
K. Ghosh (2009). We have addressed the locally risk minimizing pricing of
European type options. In a recent paper with two students Goswami et al. (2016), I have studied the same problem
for a more general class of SM processes. This class can be termed as the
class of semiMarkov processes with agedependent transitions whereas the one
which appeared in 2009 can be termed as the class of semiMarkov processes
with ageindependent transitions. In both of the papers, all the model
parameters depend on a single SM process. Next we consider a componentwise
semiMarkov process (CSM), which is a wider class of pure jump processes than
those mentioned above. Under such asset price model we derive the option
price equation (generalization of BSM PDE) and provide the classical solution
in Das et al. (2018). The sensitivity of the call option price to the
calibration error in the transition rate of SM process is studied with S. Nandan (2016). Recently, the European type option pricing
in SM generalization of the Heston's stochastic
volatility model is carried out with A. Biswas (2018). Again we successfully
derive the pricing equation (a generalization of Heston's
PDE) and provide its classical solution. With two other students O. Manjarekar and A. ramachandran
(2018) I have investigated option pricing in a jumpdiffusion (JD) model with
SM switching. JD is a very successful model for the asset price for
incorporating jump discontinuities, giving rise to a heavy tail distribution of
return. 
Past and present research
students:
Name 
Affiliation 
Project
type 
Duration 
Placement 
IIT
Kan 
summer 
June’12July’12 
Analyst
in HSBC 

IISER
P 
MS
dissertation 
Aug’12Mar’14 
MBA
in IIM Lucknow 

MSc
dissertation 

CURaj 
MSc
dissertation 







Anjana Ramachandran 
Univ
of Botswana 
Doctoral 
Oct’16Present 

Sanjay N. S. 
IISER
P 
MS
dissertation 
May’18present 

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