**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

Time: 6pm-7pm

**Location**:

UCL in Torrington Place 1-19 Room 102

**Course summary**:

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

**Location**:

Room: KSW 1.04 (20 Kingsway), LSE

Map and direction can be found here: http://www.lse.ac.uk/mapsAndDirections/findingYourWayAroundLSE.aspx

**Prerequisites**:

A background in stochastic calculus

**Course summary:**

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.

**Indicative readings:**

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

**Location**:

Cass building, 106 Bunhill Row, EC1Y 8TZ

**Important:**

In order to gain access to the building, students need to register beforehand. Please get registered before March 1.

**Outline:**

1. Levy processes

- Definition

- 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'

- PIDE

- 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**:

Dates: March 28 and April 3, 10, 19 and 24, 2017. These are all
Mondays, except March 28 (Tuesday)
and April 19 (Wednesday).

Times: 2pm - 5pm (all five dates). 15 hours in total.

Times: 2pm - 5pm (all five dates). 15 hours in total.

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

https://www.union.ic.ac.uk/scc/speakersclub/?page_id=204

**Course summary:**

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.

Course page like: http://wwwf.imperial.ac.uk/~dbrigo/doctoralICmaths/index.html

**MF12 Incomplete Markets**

**Lecturer**: Dr. Teemu Pennanen, King's College

**Time and dates**:

Wednesdays 4-6pm, weeks 21 to 31 starting on January 18

**Location**:

Strand campus, King's College London, S-2.23

**Aims**:

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.

**Outline:**

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.