Info

I received my Bachelor's degree in Mathematics from St. Xavier's College, Calcutta in 2002. In the same year, I joined the Integrated Ph.D. program in the Department of Mathematics of 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 the best performance in the National Eligibility Test in Mathematical Sciences. My MS thesis was titled “Controlled Semi-Markov Processes with Partial Observation”. I was bestowed with a Doctorate degree from the Department of Mathematics, IISc in the year 2008 under the supervision of Prof. M. K. Ghosh (Link to my Ph.D. thesis-“Semi-Markov Processes in Dynamic Games and Finance”). In the following three years, I carried out my postdoctoral research at 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 the fall of 2011. Since then, I have offered a variety of graduate and undergraduate courses- Multivariable Calculus, Point-set Topology, Measure Theory, Functional Analysis, Numerical Analysis, Probability Theory, Stochastic Processes, Probabilistic methods in PDE, Mathematical Finance, to name a few. I was reappointed at the same department as an Associate Professor in spring, 2018. I was awarded a joint appointment in the Data Science department in 2022 for the next five years. My current research interest comprises Non-cooperative Stochastic Dynamic Game, Stochastic Control, Mathematical Finance, and Queueing Networks. So far, I have coauthored many peer-reviewed research articles published in well-reputed journals including J. Math. Anal. Appl., Electron. Commun. Probab., J. Theoret. Probab., SIAM J. Control Optim., Appl. Math. Optim., Statist. Probab. Lett., Int. J. Financ. Eng., J. Math. Econom., and Stoch. Anal. Appl. I am an invited reviewer of Mathematical Reviews, published by the American Mathematical Society, and I also regularly take up refereeing responsibility from several Mathematics journals and book publishers. Apart from academic research, I also take up industrial research by collaborating with practitioners.

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 the long memory effect, stochastic volatility, heavy-tail distribution of log return, jump discontinuities of the asset price, etc. In the classical model of stock prices by Black-Scholes-Merton(BSM), which is assumed to be Geometric Brownian Motion (GBM), the drift and the volatility of the prices are held constant. However, in reality, the empirical volatility varies over time. In the 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 a finite-state Markov regime is a very popular choice. In comparison with Markov switching, the study of semi-Markov (SM) regime switching is relatively uncommon. In such models, one has an opportunity to incorporate some memory effects of the market. In particular, the knowledge of past stagnancy duration can be fed into the option price formula to obtain the price value. Hence this these models have 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 jointly with Mrinal K. Ghosh (2009). We have addressed the locally risk minimizing pricing of European options. In a paper with two students (2016), I studied the same problem for a more general class of SM processes. This class can be termed as the class of semi-Markov processes with age-dependent transitions whereas the one which appeared in 2009 can be termed as the class of semi-Markov processes with age-independent transitions. In both of the papers, all the model parameters depend on a single SM process. Next, we consider a component-wise semi-Markov process (CSM), which is a wider class of pure jump processes than those mentioned above. Under such an asset price model we derive the option price equation (a 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 the SM process was studied with S. Nandan (2016). The European style option pricing in SM generalization of Heston's stochastic volatility model was carried out in Biswas et al. (2018). Again we successfully derive the pricing equation (a generalization of Heston's PDE) and provide its classical solution. A model-free data-driven option pricing was solved with two undergrad students in 2021. In a recent work Chatterjee et al (2023), we found the fair price of some Asian options under SM modulated GBM market model. With two other students, I investigated option pricing in a jump-diffusion (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. In various other works with students and collaborators, I have investigated the computational aspects of option pricing too.