Department of
Mathematics

Anindya Goswami received BSc in Mathematics from St. Xavier's College, Calcutta. He joined the Integrated PhD program in the Department of Mathematics at the Indian Institute of Science, Bangalore from where he received PhD in 2008. In the following three years, he carried out postdoctoral research at the University of Twente, Netherlands; INRIA- Rennes, France; and Technion- Israel Institute of Technology, Israel.  He joined IISER Pune as an Assistant Professor in the Fall of 2011.

Research

Mathematical finance, stochastic processes and control

One of the research goals pursued by Dr. Anindya Goswami 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 Black-Scholes-Merton(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 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 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. Under such asset price model and its further extensions, they derive the option price equation (generalization of BSM PDE) and provide the classical solution. The group is also addressing the relevant model calibration problems.

Selected Publications

Goswami, A. Rana, N. and Siu, T. K. (2022). Regime switching optimal growth model with risk sensitive preferences. Journal of Mathematical Economics 101:102702.

Goswami, A. Rajani S. and Tanksale A. (2021). Data-driven option pricing using single and multi-asset supervised learning. International Journal of Financial Engineering 08:2141001.

Das, M., Goswami, A. and Rana, N. (2018). Risk sensitive portfolio optimization in a jump diffusion model with regimes. SIAM J. Control Optim. 56:1550-1576

Atar, R., Goswami, A. and Shwartz, A. (2013). Risk-sensitive control for the parallel server model. SIAM Journal on Control and Optimization 51:4363-4386.

Ghosh, M.K. and Goswami, A. (2009). Risk minimizing option pricing in a semi-Markov modulated market. SIAM Journal on Control and Optimization 48:1519-1541.