Convener(s)
| Name: | Prof Subhamay Saha | Prof. Chandan Pal |
| Mailing Address: | Associate Professor, Department of Mathematics, IIT Guwahati, Assam, 781039. |
Associate Professor, Department of Mathematics, IIT Guwahati, Assam, 781039. |
| Email: | saha.subhamay at iitg.ac.in | cpal at iitg.ac.in |
Most real life phenomena evolve in a random fashion. In order to model such random evolution, we need the mathematical tool called stochastic processes. Martingales form a very important class of stochastic processes. In this advanced instructional school, we would like to cover the basics of discrete and continuous parameter martingales.
Another very important tool in probability theory is stochastic calculus. During the school the students will be introduced to stochastic calculus. First they will learn about Brownian motion, followed by definition and properties of Ito integration.
The focus will then shift to the applications of the above topics to the domain of mathematical finance. In this part the students will be introduced to various financial instruments. They will learn about option pricing theory both in discrete and continuous time. Finally they will be introduced to portfolio optimization theory.
Martingales and stochastic calculus part will have approximately 20 hours of lectures and finance part will have approximately 16 hours of lectures. This school is targeted towards post graduate and Ph.D students of science and engineering. Basic knowledge of probability and measure theory will be assumed.
Dates:
Venue:
Venue Address:
Department of Mathematics,
Indian Institute of Technology Guwahati,
Assam, 781039.
BITS Pilani, KK Birla Goa Campus NH-17B, Zuarinagar
Goa-403726
Venue State:
Venue City:
PIN:
Syllabus:
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Dr. Koushik Saha IIT Bombay
|
6 hrs |
Definition and examples of discrete parameter martingales; Doob-Meyer decomposition, optional stopping theorems; martingale convergence theorems, uniform integrability. |
|
Prof. Parthanil Roy IIT Bombay
|
6 hrs |
Definition of Brownian motion, sample path properties; strong Markov property, reflection principle; Definition and examples of continuous parameter martingales, Doob-Meyer decomposition, continuous square integrable martingales, quadratic variation, exponential martingales. |
|
Dr. Manjunath Krishnapur IISc. Bangalore |
6 hrs |
Definition of Ito integration, properties of Ito integral, Ito’s isometry, Ito-Doeblin formula; Existence and Uniqueness of stochastic differential equations, Feynman-Kac formula. |
|
Prof. Siddhartha P. Chakrabarty IIT Guwahati |
6 hrs |
Introduction of financial derivatives: forwards, futures, options. No arbitrage principle, put-call parity; Markowitz mean-variance portfolio optimization, efficient frontier, Capital asset pricing model. |
|
Dr. Subhamay Saha IIT Guwahati |
6 hrs |
Option pricing theory in discrete-time: Binomial model, pricing of European and American Options, finite market model, fundamental theorems of asset pricing. |
|
Dr. Chandan Pal IIT Guwahati |
6 hrs |
Option pricing theory in continuous-time: Black Scholes Merton model, derivation and solution of Black Scholes pde, risk-neutral pricing, Girsanov’s theorem and Martingale representation theorem, fundamental theorems of asset pricing. |
References:
1. D. Williams, Probability with Martingales, Cambridge University Press, 1991.
2. R. Durrett, Probability: Theory and Examples, Cambridge University Press, 2019.
3. I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1998.
4. P. Baldi, Stochastic Calculus: An Introduction through Theory and Exercises, Springer, 2017.
5. M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, Springer, 2011.
6. S. E. Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer, 2004.
7. S. E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Bivakar Bose |
IIT Guwahati |
|
2 |
Amit Ghosh |
IIT Guwahati |
|
3 |
Pratim Dey |
IIT Guwahati |
Time Table:
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05 –11.25) |
Lecture 2 (11.30–1.00) |
Lunch (1.05 |
Tutorial (2.30–3.30) |
Tea (3.35-3.55) |
Tutorial (4.00-5.00) |
Snacks 5.05-5.30 |
|
|
|
(name of the speaker |
|
(name of the speaker |
|
(name of the speaker + tutors) |
|
(name of the speaker + tutors) |
|
|
Mon |
11/05 |
DTM-1(KS) |
|
BM&CTM-1 (PR) |
|
KS+PD+AG |
|
PR+PD+AG |
|
|
Tues |
12/05 |
DTM-2(KS) |
|
BM&CTM-2 (PR)) |
|
KS+PD+AG |
|
PR+PD+AG |
|
|
Wed |
13/05 |
DTM-3(KS) |
|
BM&CTM-3 (PR) |
|
KS+PD+BB |
|
PR+BB+AG |
|
|
Thu |
14/05 |
DTM-4(KS) |
|
BM&CTM-4 (PR) |
|
KS+BB+AG |
|
PR+BB+PD |
|
|
Fri |
15/05 |
SC-1(MK) |
|
IFE-1(SPC) |
|
MK+BB+AG |
|
SPC+PD+BB |
|
|
Sat |
16/05 |
SC-2(MK) |
|
IFE-2(SPC) |
|
MK+PD+AG |
|
SPC+BB+AG |
|
|
SUNDAY: OFF |
|||||||||
|
Mon |
18/05 |
SC-3(MK) |
|
IFE-3(SPC) |
|
MK+AG+BB |
|
SPC+BB+PD |
|
|
Tues |
19/05 |
SC-4(MK) |
|
IFE-4(SPC) |
|
MK+BB+PD |
|
SPC+BB+AG |
|
|
Wed |
20/05 |
OPD-1(SS) |
|
OPC-1(CP) |
|
SS+PD+AG |
|
CP+PD+BB |
|
|
Thu |
21/05 |
OPD-2(SS) |
|
OPC-2(CP) |
|
SS+PD+AG |
|
CP+AG+BB |
|
|
Fri |
22/05 |
OPD-3(SS) |
|
OPC-3(CP) |
|
SS+PD+AG |
|
CP+PD+BB |
|
|
Sat |
23/05 |
OPD-4(SS) |
|
OPC-4(CP) |
|
SS+BB+PD |
|
CP+AG+BB |
|
DTM- Discrete-time Martingales
BM&CTM – Brownian Motion and Continuous-time Martingales
SC- Stochastic Calculus
IFE- Introduction to Financial Engineering
OPD- Option Pricing in Discrete-time
OPC- Option Pricing in Continuous-time
Full forms for the abbreviations of speakers and tutors:
PR: Parthanil Roy
KS: Koushik Saha
SS: Subhamay Saha
CP: Chandan Pal
SPC: Siddhartha P. Chakrabarty
MK: Manjunath Krishnapur
PD: Pratim Dey
AG: Amit Ghosh
BB: Bivakar Bose
Selected Applicants:
| Sr.n | SID | Full Name | Gender | Affiliation | Position in College/ University | University/Institute M.Sc./ M.A. | Year of Passing M.Sc./ M.A | Ph.D. Degree Date |
| 1 | 67360 | Ms. Sanjava Reena Govindbhai | Female | Department Of Mathematics, Sardar Patel University | PhD | Department of mathematics, Sardar Patel University | 2022 | |
| 2 | 67388 | Mr. Ashutosh Kasaudhan | Male | Indian Institute of Technology (BHU) Varanasi | PhD | Indian Institute of Technology Bhubaneswar | 2024 | |
| 3 | 67390 | Mr. Gaurav G Kottari | Male | Shiv Nadar Institute of Eminence | PhD Student | Mangalore University | 2022 | |
| 4 | 67403 | Ms. Shikha Khatri | Female | Indian Institute of Technology, Roorkee | PhD | Hemvati Nandan Bahuguna Garhwal University | 2022 | |
| 5 | 67408 | Mr. Sougata Das | Male | IIT KHARAGPUR | PhD Student | IISER KOLKATA | 2025 | |
| 6 | 67413 | Ms. Shalini Beniwal | Female | Indian Institute of Technology Jammu | PhD Student | Panjab University, Chandigarh | 2022 | |
| 7 | 67419 | Mr. Mohit Lamba | Male | Central University of Punjab | Research Scholar (Ph.D.) | Central University of Punjab | 2022 | |
| 8 | 67458 | Mr. Shyan Ghosh | Male | Indian Institute of Technology Bhilai | Ph.D. Student | University of Calcutta | 2022 | |
| 9 | 67460 | Mr. Akram Khan | Male | Indian Institute of Technology Roorkee | PhD | Indian Institute of Technology Kharagpur | 2024 | |
| 10 | 67465 | Ms. Khushi Anil Mittal | Female | Indian Institute of Technology, Indore | Msc Student | Indian Institute of Technology, Indore | 2026 | |
| 11 | 67466 | Ms Samra Naaz | Female | Indian Institute of Science Education and Research Bhopal | Integrated PhD Student | Indian Institute of Science Education and Research Bhopal | ||
| 12 | 67470 | Ms. Naina Aggarwal | Female | Indian Institute of Technology, Roorkee | Ph.D | Indian Institute of Technology, Roorkee | 2025 | |
| 13 | 67472 | Mr. Harsh Tiwari | Male | Indian Institute of Technology Roorkee | PhD | Banaras Hindu University | 2024 | |
| 14 | 67484 | Ms. Kiranpreet Kaur | Female | Indian Institute of Technology Ropar | PhD | Panjab University M.Sc. | 2023 | |
| 15 | 67500 | Mr Suresh Mondal | Male | Indian Institute of Technology Roorkee | PhD | Indian Institute of Technology Kanpur | 2025 | |
| 16 | 67502 | Ms. Jyoti Dhiman | Female | IIT Bombay | Project Associate | M.Sc. | 2025 | |
| 17 | 67505 | Mr. Shubham Kumar Singh | Male | Indian Institute of Technology Bombay | PhD | IIT Patna | 2023 | |
| 18 | 67518 | Mr Dheeraj Sharma | Male | Indian Institute of technology tirupati | MSc Student | Indian institute of technology tirupati | Appeared / Awaiting Result | |
| 19 | 67548 | Mr. Amit Kumar Behera | Male | National Institute of Technology | Phd | FAKIR MOHAN UNIVERSITY,BALASORE,ODISHA | 2022 | |
| 20 | 67626 | Ms. Shreya Pandey | Female | Indian Institute of Science Education and Research, Pune | Int. PhD Student | |||
| 21 | 67627 | Mr. Souvik Mondal | Male | IIT Madras | Project Associate | Indian Association for the Cultivation of Science (IACS) | 2024 | |
| 22 | 67838 | Mr. Keshav Kumar | Male | Indian Institute of Technology Bombay | PhD | Indian Institute of Science Education and Research Bhopal | 2021 | |
| 23 | 67856 | Mr. Tushar Satishbhai Hemani | Male | IIT MADRAS | PhD | IIT DELHI | 2025 | |
| 24 | 67875 | Mr. Md Rahil Miraj | Male | Indian Statistical Institute, Kolkata | M.Stat student | Indian Statistical Institute, Kolkata | Appeared / Awaiting Result | |
| 25 | 67912 | Ms. Jyoti Pandey | Female | Shailesh J. Mehta School of Management, IIT Bombay | Research Scholar | University of Delhi (M.Com) | 2019 | |
| 26 | 67914 | Mr. Shaswat Bhaskar | Male | Indian Statistical Institute Kolkata | MSc Student | Indian Statistical Institute | Appeared / Awaiting Result | |
| 27 | 67984 | Mr. A Vignesh | Male | Bharathiar University | PhD Student | Bharathiar University, Coimbatore -46, India | 2023 | |
| 28 | 67993 | Mr. Dinesh Karthik Mulumudi | Male | Indian Institute of Science Education and Research (IISER) Pune | 4th Year BS-MS Student | Not Applicable | ||
| 29 | 68047 | Mr. Kaustabh Roy | Male | Indian Institute of Technology (IIT) , Kanpur | M.Sc. Student in Statistics | Indian Institute of Technology(IIT) , Kanpur | Appeared / Awaiting Result | |
| 30 | 68071 | Mr. Saptarshi Sinha | Male | Indian Statistical Institute | PhD | Indian Statistical Institute, Kolkata | 2025 | |
| Local | ||||||||
| 1 | 67433 | Mr. Krishna Mani Nath | Male | Gauhati University | PhD Student | Gauhati University | 2023 | |
| 2 | 67444 | Mr Jugal Kishore Deka | Male | Gauhati University | PhD student | Gauhati University | 2023 | |
| 3 | 67534 | Mr Sayan Dhan | Male | IIT Guwahati | PhD | BHU | 2025 | |
| 4 | 67603 | Mr. Debottam Ghosh | Male | IIT Guwahati | MTech Student | IIT Hyderabad | 2024 | |
| 5 | 67819 | Ms Bratati Pal | Female | IIT Guwahati | PhD student | CALCUTTA UNIVERSITY | 2022 | |
| 6 | 68073 | Mr. Pranab Jyoti Hazarika | Male | Gauhati University | PhD | Tezpur Central University | 2020 | |
| Waitlisted | ||||||||
| 1 | 67636 | Mr Santhakumar V | Male | Indian Institute of Technology Bombay | PhD | Indian Institute of Technology Bombay | 2025 | |
| 2 | 67407 | Mr. Raj Karan Gupta | Male | Indian Institute of Technology Roorkee | PhD | Banaras Hindu University | 2022 | |
| 3 | 67422 | Mr. Poleen Kumar | Male | Indian Institute of Technology (BHU) | PhD | Guru Nanak Dev University, Amritsar | 2020 | |
| 4 | 67423 | Ms. Savita Chaturvedi | Female | Indian Institute of Technology (BHU) | PhD | Indian institute of Technology(Indian School of Mines) Dhanbad | 2018 | |
| 5 | 67436 | Mr. Agniva Dey | Male | Ramakrishna Mission Vivekananda Centenary College | PhD | West Bengal State University | 2023 | |
| 6 | 67457 | Ms. Rohini Bhagwanrao Pote | Female | Indian Institute of Technology Bhilai | PhD Student | Savitribai Phule Pune University | 2021 | |
| 7 | 67586 | Mr Harsh Jaiswal | Male | IIT Tirupati | ||||
| 8 | 67822 | Mr. Gaurav Kandpal | Male | IIT kharagpur | ||||
| 9 | 67950 | Ms. Saipriya Dubey | Female | Chennai Mathematical Institute | ||||
How to Reach:
TBA