Past Reading Groups Math Finance
Topic: Optimal Transportation in Finance
Location: Room 139, Huxley Building.
Date & Time: Wednesdays, 3pm - 4pm
Organisers: Daphne Liu and Patrick Roome
Term 1: Theory ([1], pp. 1-104)
| Date | Speaker | Content |
|---|---|---|
| 9/10/2013 | Patrick Roome | Introduction and overview ([1], pp. 1-20) |
| 16/10/2013 | Daphne Liu | Proof of the Kantorovich duality I ([1], pp. 21-25) |
| 23/10/2013 | Grzegorz Andruszkiewicz | Proof of the Kantorovich duality II ([1], pp. 25-34) |
| 30/10/2013 | Geraldine Bouveret | Duality-based proof of Brenier's theorem I ([1], pp. 47-66) |
| 6/11/2013 | Eric Schaanning | Duality-based proof of Brenier's theorem II ([1], pp. 66-72) |
| 13/11/2013 | Sergey Badikov | Optimal transport on the real line ([1], pp. 73-78) |
| 20/11/2013 | Ivo Mihaylov | Cyclical monotonicity and Brenier's theorem III ([1], pp. 78-84) |
| 27/11/2013 | Francesco Patacchini | Generalisations to other costs ([1], pp. 85-94, [3b], [3c]) |
| 4/12/2013 | Hao Liu | The distance case and properties of c-concave functions ([1], pp. 97-104, [3a], [3b]) |
| 11/12/2013 | Problem Class | Exercises: 1.11, 2.14, 2.21, 2.35, 2.41. (A few more on email) |
Term 2: Finance applications ([4a],[4b],[4c],[4d])
| Date | Speaker | Content |
|---|---|---|
| 22/01/2014 | Patrick Roome | Overview for term |
| 29/01/2014 | Sergey Badikov | ([4a], pp. 1-6) |
| 05/02/2014 | Daphne Liu | ([4a], pp. 7-17) |
| 12/02/2014 | Eric Schaanning | ([4b], pp. 1-13) |
| 19/02/2014 | Sergey Badikov |
([4b], pp. 13-29) |
| 26/02/2014 | Geraldine Bouveret |
([4c], pp. 1-9) |
| 05/03/2014 | Patrick Roome |
([4c], pp. 9-18) |
| 12/03/2014 | Francesco Patacchini |
([4d], pp. 1-5) |
| 19/03/2014 | Hao Liu | ([4d], pp. 5-10) |
| 26/03/2014 | Numerical Implementation Class |
References:
[1] C. Villani. Topics in Optimal Transportation. American Mathematical Society (2003).
[2] C. Villani. Optimal Transport, Old and New. Springer (2008).
[3] (a) Evans, (b) GangboMcCann96, (c) ExactSolutionsMcCann, Videos.
[4] Finance applications:
- Kantorovich duality with martingale constraints: (a) BHP13.
- Brenier's theorem with martingale constraints: (b) HT13, BJ13.
- Martingale optimal transport plans for specific products: At-the-money forward straddle [(c) HK13, HN08], Lookback option [GHT11, HOST13].
- Numerical methods: (d) PHL11.
- Continuous-time versions of the problem: SD13, TT13.
- A constrained martingale optimal transport problem: PHL13.
- Other material: Mini Courses, T13, K13, MK13, BLS13.
[5] Background material:
(a) H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer (2011).
(b) R.T. Rockafellar. Convex Analysis . Princeton University Press (1970).
Topic: Stochastic Control
PLEASE NOTE: READING GROUP TAKES PLACE 3-4PM ON 25/02/2015
Location: Room 642, Huxley Building.
Date & Time: Wednesdays, 4pm - 5pm
Organiser: Ivo Mihaylov and Sergey Badikov
Autumn Term
| Date | Speaker | Content | |
|---|---|---|---|
| 15/10/2014 | Ivo Mihaylov | [1] Up to Chapter 3.2 | |
| 22/10/2014 | Eamon McMurray | [1] Chapter 3.3 onwards | |
| 29/10/2014 | Sergey Badikov | [1] Chapter 7 - Martingale and Convex Duality methods | |
| 5/11/2014 | Hao Liu | [1] Chapter 4 - Viscosity solutions | |
| 12/11/2014 | Simon Ellersgaard | [1] Chapter 4 (4.4 onwards) | |
| 19/11/2014 | Arman Khaledian | [1] Chapter 6 BSDEs | |
| 26/11/2014 | Ryan Wong | [1] Chapter 6 BSDEs (second half) | |
| 3/12/2014 | Pierre Blacque | [1] Chapter 5 Optimal Stopping | |
| 10/12/2014 | Spyros Kollias Liapis | [2] (Ch. 3-5) Control in Partially observable systems |
Spring Term
| Date | Speaker | Content | |
|---|---|---|---|
| 28/01/2015 | Sergey Badikov | Uncertain Volatility Model, [3] Chapter 5.2 and Chapter 9 | |
| 04/02/2015 | Simon Ellersgaard | Optimal Trade Execution, [4] and [5] | |
| 11/02/2015 | Pierre Blacque | On Viscosity Solutions of Path Dependent PDEs [6] | |
| 18/02/2015 | Arman Khaledian | Second Order BSDEs and Fully Nonlinear Parabolic PDEs [7] | |
| 25/02/2015 | Ivo Mihaylov | Second Order BSDEs and Fully Nonlinear Parabolic PDEs [7] | |
| 04/03/2015 | Cancelled | Cancelled due to Imperial-ETH workshop on Mathematical Finance (04.03.15-06.03.15) | |
| 11/03/2015 | Fangwei Shi | A large deviations approach to optimal long term investment [9] | |
| 18/03/2015 | Andrea Granelli | Normal approximation and Malliavin calculus | |
| 25/03/2015 | Cancelled | Cancelled |
References:
[1] H. Pham. Continuous-time Stochastic Control and Optimization with Financial Applications. Springer, volume 61 (2009).
[2] A Bain, D Crisan. Fundamentals of stochastic filtering. Springer, (2009).
[3] J. Guyon, P. Henry-Labordere. Nonlinear Option Pricing. Chapman and Hall/CRC, (2013).
[4] R. Almgren, N. Chriss. Optimal execution of portfolio transactions. Journal of Risk, (2000).
[5] A. Cartea, S. Jaimungal. Optimal execution with limit and market orders. Forthcoming: Quantitative Finance , (2014).
[6] I. Ekren et al. On Viscosity Solutions of Path Dependent PDEs. The Annals of Probability, Vol. 42, No. 1, pp. 204–236 (2014).
[7] P. Cheridito et al. Second Order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs. Communications on Pure and Applied Mathematics, v.60 (2007).
[8] B. Bouchard et al. Discrete-time approximation of BSDEs and probabilistic schemes for fully nonlinear PDEs. Radon Series Comp. Appl. Math, v.8, pp. 1-34 (2009).
[9] H. Pham A large deviations approach to optimal long term investment. Finance and Stochastics, v.7, no.2, pp. 169-195 (2003).
Past Mathematical Finance PhD Days
Topic: Optimal Transportation in Finance
Location: Room 139, Huxley Building.
Date & Time: Wednesdays, 3pm - 4pm
Organisers: Daphne Liu and Patrick Roome
Term 1: Theory ([1], pp. 1-104)
| Date | Speaker | Content |
|---|---|---|
| 9/10/2013 | Patrick Roome | Introduction and overview ([1], pp. 1-20) |
| 16/10/2013 | Daphne Liu | Proof of the Kantorovich duality I ([1], pp. 21-25) |
| 23/10/2013 | Grzegorz Andruszkiewicz | Proof of the Kantorovich duality II ([1], pp. 25-34) |
| 30/10/2013 | Geraldine Bouveret | Duality-based proof of Brenier's theorem I ([1], pp. 47-66) |
| 6/11/2013 | Eric Schaanning | Duality-based proof of Brenier's theorem II ([1], pp. 66-72) |
| 13/11/2013 | Sergey Badikov | Optimal transport on the real line ([1], pp. 73-78) |
| 20/11/2013 | Ivo Mihaylov | Cyclical monotonicity and Brenier's theorem III ([1], pp. 78-84) |
| 27/11/2013 | Francesco Patacchini | Generalisations to other costs ([1], pp. 85-94, [3b], [3c]) |
| 4/12/2013 | Hao Liu | The distance case and properties of c-concave functions ([1], pp. 97-104, [3a], [3b]) |
| 11/12/2013 | Problem Class | Exercises: 1.11, 2.14, 2.21, 2.35, 2.41. (A few more on email) |
Term 2: Finance applications ([4a],[4b],[4c],[4d])
| Date | Speaker | Content |
|---|---|---|
| 22/01/2014 | Patrick Roome | Overview for term |
| 29/01/2014 | Sergey Badikov | ([4a], pp. 1-6) |
| 05/02/2014 | Daphne Liu | ([4a], pp. 7-17) |
| 12/02/2014 | Eric Schaanning | ([4b], pp. 1-13) |
| 19/02/2014 | Sergey Badikov |
([4b], pp. 13-29) |
| 26/02/2014 | Geraldine Bouveret |
([4c], pp. 1-9) |
| 05/03/2014 | Patrick Roome |
([4c], pp. 9-18) |
| 12/03/2014 | Francesco Patacchini |
([4d], pp. 1-5) |
| 19/03/2014 | Hao Liu | ([4d], pp. 5-10) |
| 26/03/2014 | Numerical Implementation Class |
References:
[1] C. Villani. Topics in Optimal Transportation. American Mathematical Society (2003).
[2] C. Villani. Optimal Transport, Old and New. Springer (2008).
[3] (a) Evans, (b) GangboMcCann96, (c) ExactSolutionsMcCann, Videos.
[4] Finance applications:
- Kantorovich duality with martingale constraints: (a) BHP13.
- Brenier's theorem with martingale constraints: (b) HT13, BJ13.
- Martingale optimal transport plans for specific products: At-the-money forward straddle [(c) HK13, HN08], Lookback option [GHT11, HOST13].
- Numerical methods: (d) PHL11.
- Continuous-time versions of the problem: SD13, TT13.
- A constrained martingale optimal transport problem: PHL13.
- Other material: Mini Courses, T13, K13, MK13, BLS13.
[5] Background material:
(a) H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer (2011).
(b) R.T. Rockafellar. Convex Analysis . Princeton University Press (1970).
Topic: Stochastic Control
PLEASE NOTE: READING GROUP TAKES PLACE 3-4PM ON 25/02/2015
Location: Room 642, Huxley Building.
Date & Time: Wednesdays, 4pm - 5pm
Organiser: Ivo Mihaylov and Sergey Badikov
Autumn Term
| Date | Speaker | Content | |
|---|---|---|---|
| 15/10/2014 | Ivo Mihaylov | [1] Up to Chapter 3.2 | |
| 22/10/2014 | Eamon McMurray | [1] Chapter 3.3 onwards | |
| 29/10/2014 | Sergey Badikov | [1] Chapter 7 - Martingale and Convex Duality methods | |
| 5/11/2014 | Hao Liu | [1] Chapter 4 - Viscosity solutions | |
| 12/11/2014 | Simon Ellersgaard | [1] Chapter 4 (4.4 onwards) | |
| 19/11/2014 | Arman Khaledian | [1] Chapter 6 BSDEs | |
| 26/11/2014 | Ryan Wong | [1] Chapter 6 BSDEs (second half) | |
| 3/12/2014 | Pierre Blacque | [1] Chapter 5 Optimal Stopping | |
| 10/12/2014 | Spyros Kollias Liapis | [2] (Ch. 3-5) Control in Partially observable systems |
Spring Term
| Date | Speaker | Content | |
|---|---|---|---|
| 28/01/2015 | Sergey Badikov | Uncertain Volatility Model, [3] Chapter 5.2 and Chapter 9 | |
| 04/02/2015 | Simon Ellersgaard | Optimal Trade Execution, [4] and [5] | |
| 11/02/2015 | Pierre Blacque | On Viscosity Solutions of Path Dependent PDEs [6] | |
| 18/02/2015 | Arman Khaledian | Second Order BSDEs and Fully Nonlinear Parabolic PDEs [7] | |
| 25/02/2015 | Ivo Mihaylov | Second Order BSDEs and Fully Nonlinear Parabolic PDEs [7] | |
| 04/03/2015 | Cancelled | Cancelled due to Imperial-ETH workshop on Mathematical Finance (04.03.15-06.03.15) | |
| 11/03/2015 | Fangwei Shi | A large deviations approach to optimal long term investment [9] | |
| 18/03/2015 | Andrea Granelli | Normal approximation and Malliavin calculus | |
| 25/03/2015 | Cancelled | Cancelled |
References:
[1] H. Pham. Continuous-time Stochastic Control and Optimization with Financial Applications. Springer, volume 61 (2009).
[2] A Bain, D Crisan. Fundamentals of stochastic filtering. Springer, (2009).
[3] J. Guyon, P. Henry-Labordere. Nonlinear Option Pricing. Chapman and Hall/CRC, (2013).
[4] R. Almgren, N. Chriss. Optimal execution of portfolio transactions. Journal of Risk, (2000).
[5] A. Cartea, S. Jaimungal. Optimal execution with limit and market orders. Forthcoming: Quantitative Finance , (2014).
[6] I. Ekren et al. On Viscosity Solutions of Path Dependent PDEs. The Annals of Probability, Vol. 42, No. 1, pp. 204–236 (2014).
[7] P. Cheridito et al. Second Order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs. Communications on Pure and Applied Mathematics, v.60 (2007).
[8] B. Bouchard et al. Discrete-time approximation of BSDEs and probabilistic schemes for fully nonlinear PDEs. Radon Series Comp. Appl. Math, v.8, pp. 1-34 (2009).
[9] H. Pham A large deviations approach to optimal long term investment. Finance and Stochastics, v.7, no.2, pp. 169-195 (2003).