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, IIT Guwahati, Assam, 781039.
Venue State:
Venue City:
PIN:
Syllabus:
Detailed 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 (1.05–2.25) |
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:
How to Reach:
TBA