MF20 A Statistical Perspective on Data Analytics and Machine Learning Techniques for Insurance and Risk Management
Lecturer: Dr. Gareth Peters, UCL
Time and dates:
13th Jan - lecture 1
10th Feb - lecture 2
24th Feb - lecture 3
24th March - lecture 4
UCL in Torrington Place 1-19 Room 102
1. Statistical Overview of regression, classification and Bayesian Modelling for Insurance and Risk management.
2. Topics in non-life insurance and emergence of Usage Based Insurance
3. Topics in Catastrophe insurance
4. Topics in Risk management and Operation Risk
MF26 Local Martingales and the martingale property
Lecturer: Dr. Johannes Ruf, LSE
Time and dates:
Spring term : Mondays, Weeks 2,3,4,5,7,9,10 beginning on January 16
Time: 18.00 to 20.30
Room: KSW 1.04 (20 Kingsway), LSE
Map and direction can be found here: http://www.lse.ac.uk/mapsAndDirections/findingYourWayAroundLSE.aspx
A background in stochastic calculus
Introduction and properties of local martingales. Examples for strict local martingales, including local martingales with jumps. How to generate strict local martingales in a systematic way. Review of different methods and their proofs to decide on martingale property; in particular, methods based on weak tails and Novikov-type conditions.
References to start reading, available on http://www.oxford-man.ox.ac.uk/~jruf/
1) Hulley & Ruf: Weak tail conditions for local martingales (2015).
2) Blanchet & Ruf: A weak convergence criterion for constructing changes of measure, Stochastic Models (2015).
3) Ruf: The martingale property in the context of stochastic differential equations, Electronic Communications in Probability,
Volume 20, Issue 34 (2015).
MF13 Levy Processes and Applications in Finance
Lecturer: Dr. Laura Ballotta, Cass
Time and dates:
All classes are from 3 to 6 pm
Room 6001 - Wednesday 15/03/2017
Room 2007 - Wednesday 22/03/2017
Room 2007 - Wednesday 29/03/2017
Room 2007 - Wednesday 5/04/2017
Room 2007 - Thursday 6/04/2017
Cass building, 106 Bunhill Row, EC1Y 8TZ
In order to gain access to the building, students need to register beforehand. Please get registered before March 1.
1. Levy processes
- From infinitely divisible distributions to Levy processes
- Levy-Khintchine representation
- Levy decomposition
- Fine structure of the Jump process
2. Classes of Levy processes used in Finance
- Jump Diffusion processes
- Subordinated Brownian motions
- An example: fitting distributions
3. Option pricing
- Ito's Lemma and the replicating portfolio - market incompleteness part I
- Girsanov Theorem and Risk Neutral Valuation - market incompleteness part II
- Pricing vanilla options and `semi-closed analytical formulae'
- Applications: when does it matter? Tail events - credit risk modelling and VaR of derivatives positions
- Shortcomings of Levy processes and moving forward: Time Changed Levy processes
4. Simulation and other computation issues
- Monte Carlo simulation: plain vanilla strategy
- Some variance reduction via stratification: bridge strategy
- Fourier transforms
- An example: COS method
5. Linear transformation and correlated Levy processes
- Levy processes in Rd
- Linear transformation
- Margin processes
- The case of the sum of independent Levy processes
- Correlated Levy processes via subordination
- Correlated Levy processes via linear transformation
- Applications: parameter estimation, calibration, implied correlation
MF17 Nonlinear Valuation under Credit Gap Risk, Initial and Variation Margins and Funding Costs
Lecturer: Dr. Damiano Brigo, Imperial
Time and dates:
Imperial College London, South Kensington campus, Department of Mathematics, Huxley Building, Lecture room 130. The department is located at 180 Queen's Gate, SW7 2AZ. Directions to the lecture
theatre 130 are given here
The market for financial products and derivatives reached an outstanding notional size of 708 USD Trillions in 2011, amounting to ten times the planet gross domestic product. Even discounting double counting, derivatives appear to be an important part of the world economy and have played a key role in the onset of the financial crisis in 2007. After briefly reviewing the Nobel-awarded option pricing paradigm by Black Scholes and Merton, hinting at precursors such as Bachelier and de Finetti, we explain how the self-financing condition and Ito's formula lead to the Black Scholes Partial Differential Equation (PDE) for basic option payoffs. We hint at the Feynman Kac theorem that allows to interpret the Black Scholes PDE solution as the expected value under a risk neutral probability of the discounted future cash flows, and explain how no arbitrage theory followed. Following this quick introduction, we describe the changes triggered by post 2007 events. We re-discuss the valuation theory assumptions and introduce valuation under counterparty credit risk, collateral posting, initial and variation margins, and funding costs. We explain model dependence induced by credit effect, hybrid features, contagion, payout uncertainty, and nonlinear effects due to replacement closeout at default and possibly asymmetric borrowing and lending rates in the margin interest and in the funding strategy for the hedge of the relevant portfolio. Nonlinearity manifests itself in the valuation equations taking the form of semi-linear PDEs or Backward SDEs. We discuss existence and uniqueness of solutions for these equations. We also present a high level analysis of the consequences of nonlinearities, both from the point of view of methodology and from an operational angle. We discuss the Modigliani Miller theorem and whether this really implies that funding costs should be zero at overall institution level. Finally, we connect these developments to interest rate theory under multiple discount curves, thus building a consistent valuation framework encompassing most post-2007 effects.
MF12 Incomplete Markets
Lecturer: Dr. Teemu Pennanen, King's College
Time and dates:
Wednesdays 4-6pm, weeks 21 to 31 starting on January 18
Strand campus, King's College London, S-2.23
This module aims to give students an understanding of the main issues in the valuation and hedging of financial products in incomplete markets and to give them an introduction to convex analysis relevant in mathematical analysis of such problems.
Optimal investment and valuation of contingent claims in incomplete financial markets with transaction costs, illiquidity effects and portfolio constraints. Basic properties of convex sets and functions. Convex duality, martingale measures, state-price densities and model calibration will also be discussed.