AIS - Martingales and Stochastic Calculus with Applications to Finance
Speakers and 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