# Joint Risk & Stochastics and Financial Mathematics seminar series

One should really think of Statistics as a discipline which can be used to support other disciplines

The series aims to promote communication and discussion of research in the mathematics of insurance and finance and their interface, to encourage interaction between practice and theory in these areas, and to support academic students in related programmes at postgraduate level.

LSE maps and directions

All are welcome to attend these seminars. If you are attending from outside LSE please notify Penny Montague so that we can ensure you have access to the seminar room.

## 08/05/2019 - Guy Flint

Wednesday 8th May 2019
32L.G.08 (32 Lincoln’s Inn Fields) 12pm to 1pm
(NOTE: change of day and venue)

Guy Flint (G-Research)

Title: A primer on rough path theory

Stochastic differential equations provide a way to describe the evolution of a multidimensional system affected by some stochastic input signal:

$dy_t = V(y_t)\, dx_t, \, \, \, y_0 = \xi \in \mathbb{R}^q.$

As it is random, $x = (x_t) \subset\mathbb{R}^d$ is typically highly oscillatory and thus far from differentiable. Traditionally we can use It\^{o} calculus to define a solution to the differential equation but the It\^{o} mapping, $\pi = (\pi_t) : x \mapsto y$, is not continuous in the uniform topology unless $d=1$ or we impose very restrictive conditions on the vector field $V$. For example, given two correlated Brownian motions $W_1,W_2$, stochastic calculus cannot be used to make useful quantitative statements about the difference in their outputs:

$\sup_{t\in [0,1]} \| \pi_t(W_1) - \pi_t(W_2) \|.$

Rough path theory solves this predicament by lifting the original input $x$ into a path in a higher-dimensional Lie group. This so-called rough path encodes enough extra information to make such continuity statements precise. In fact, the estimates can be factored into deterministic and stochastic parts which has enabled simple proofs of fundamental results in stochastic analysis as well as providing the motivating example for the theory of regularity structures, (the latter was used in Martin Hairer's Fields medal-winning work on the KPZ equation).

This talk aims to provide a primer on the main ideas of rough path theory. With a minimum of Lie group theory, we hope to show some examples on how rough paths can be used by the non-specialist.

## 04/04/2019 - Michael Kupper

Thursday 4th April 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Michael Kupper (University of Konstanz)

Title: Computation of model-free hedging problems via penalization and neural networks

Abstract: We present a widely applicable approach to solving model-free hedging problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it to a finite dimensional one which corresponds to optimizing a neural network with smooth objective function. As an application we discuss a version of the martingale transport problem with homogeneous stock movements and illustrate the approach with several numerical examples. The talk is based on joint work with Stephan Eckstein.

## 28/03/2019 - Flavia Barsotti

Thursday 28th March 2019
NAB. 2.16 New Academic Building (54 Lincoln's Inn Fields) 12pm to 1pm
*change of location*

Flavia Barsotti

Title Behavioural modeling: contagion effects among customers' decisions and macroeconomic drivers

Abstract: The aim of the talk is to present a methodological approach suitable to model customers' behaviours by embedding i) correlation and contagion effects among their decisions and ii) the role of macroeconomic factors. The proposed approach is suitable to model both stable economic regimes and stress scenarios. As an example, the problem of lapse risk will be discussed. The mathematical setting assumes the lapse intensity following a dynamic contagion process with both endogenous and exogenous jump components. This allows to capture both correlation and contagion potentially arising among customers’ behaviours and the macroeconomic driver. The shot-noise intensity is then not constant and the resulting intensity process is not Markovian. Closed-form expressions and analytic sensitivities for the moments of the lapse intensity are provided, showing how lapses can be affected by massive copycat behaviours. Further analyses are then conducted to illustrate how the mean risk varies depending on the model’s parameters.

## 22/03/2019 - Oleksii Mostovyi

Friday 22nd March 2019
COL 6.15 Columbia House, (69 Aldwych) 12pm to 1pm
*change of location*

Oleksii Mostovyi (University of Connecticut)

Title: Optimal consumption from investment and labor income in a unifying framework of admissibility

Abstract: We consider a problem of optimal consumption from investment and labor income in an incomplete semimartingale market. We introduce a set of constraint times, i.e., a set of stopping times, at which the wealth process must stay positive, in a unifying way such that borrowing against the future income might be allowed or prohibited. Upon this, we increase dimensionality and treat as arguments of the value function not only the initial wealth but also a function that specifies the amount of labor income. Assuming finiteness of the primal and dual value functions and that the labor income is superreplicable  (these are essentially the minimal model assumptions), we establish the existence and uniqueness of a solution to the underlying problem and provide several characterizations of the optimizer and the value functions. This talk is based on joint work with Mihai Sirbu.

## 21/03/2019 -  Hyeng Keun Koo

Thursday 21st March 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Hyeng Keun Koo (Ajou University)

Title: Duesenberry, Long-term Wealth Management, and Asset Pricing

I will talk about Duesenberry's theory of consumption and propose a formal model of the theory. I will show how the model can be used for  long-term investors' risk management. I will also discuss asset pricing implications of the model.

## 14/03/2019 - Lukas Gonon

Thursday 14th March 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Lukas Gonon University of St. Gallen

Title: Reservoir Computing with Stochastic Inputs: Universality, Error Bounds and Financial Applications

Abstract: We study dynamic machine learning for discrete-time stochastic processes based on reservoir computing. Putting particular emphasis on echo state networks, we present results on universal approximation properties as well as error bounds for learning tasks based on these systems. Finally, we apply them to the problem of predicting realized covariances of financial time series.

The talk is based on joint works with Juan-Pablo Ortega and Lyudmila Grigoryeva.

## 28/02/2019 - Pierre-Olivier Goffard

Thursday 28th February 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Pierre-Olivier Goffard (ISFA)

Title: For a few bitcoins more

Subtitle: Fraud risk assessment within blockchain transactions

Abstract: The probability of successfully spending twice the same bitcoins is considered. A double-spending attack consists in issuing two transactions transferring the same bitcoins. The first transaction, from the fraudster to a merchant, is included in a block of the public chain. The second transaction, from the fraudster to himself, is recorded in a block that integrates a private chain, exact copy of the public chain up to substituting the fraudster-to-merchant transaction by the fraudster-to-fraudster transaction. The double-spending hack is completed once the private chain reaches the length of the public chain, in which case it replaces it. The growth of both chains are modeled by two independent counting processes. The probability distribution of the time at which the malicious chain catches up with the honest chain, or equivalently the time at which the two counting processes meet each other, is studied. The merchant is supposed to await the discovery of a given number of blocks after the one containing the transaction before delivering the goods. This grants a head start to the honest chain in the race against the dishonest chain.

A preprint is available on my website

## 14/02/2019 - Sara Svaluto-Ferro

Thursday 14th February 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Sara Svaluto-Ferro (University of Vienna)

Title: Infinite dimensional polynomial jump-diffusions

Abstract: We introduce polynomial jump-diffusions taking values in an arbitrary Banach space B via their infinitesimal generator. We obtain two representations of the (conditional) moments in terms of solution of a systems of ODEs on (R, B∗, … , (B⊗k)∗) and (R, B∗∗, … , (B⊗k)∗∗), respectively. We illustrate how the well known moment formulas for finite dimensional polynomial jump diffusions can be deduced in this general framework. As an application, we consider probability measure-valued polynomial diffusions and polynomial forward variance curve models.

## 31/01/2019 -  Hyejin Cho

Thursday 31st January 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Hyejin Cho (Université de Paris)

Title: The Order-theoretic Single Crossing Property in a One-Dimensional Screening Model

Abstract: We consider a finite one-dimensional screening of choices in monotone comparative statics (MCS). Before revealing the true state of the world, a principal sorts on actions of the agent to cause the social value of production as an informed principal. The model produces a rich order-theoretic single-crossing property according to Pick’s theorem pursuing no distortion at the top.

## 17/01/2019 - Mykhaylo Shkolnikov

Thursday 17th January 2019
CLM.7.02 Clement House, (99 Aldwych) 12pm to 1pm

Mykhaylo Shkolnikov (Princeton University)

Title : Particles interacting through the hitting times: an application to systemic risk

Abstract: I will discuss a class of particle systems that form a natural framework for the study of systemic risk. The interaction between the particles falls into the mean field framework pioneered by McKean and Vlasov in the late 1960s, but many new phenomena arise due to the singularity of the interaction. The most striking of them is the loss of regularity of the particle density caused by the self-excitation of the system, which triggers systemic crises. Mathematically, the evolution of the system can be captured initially by a suitable Stefan problem, while the following irregular behavior necessitates a more robust probabilistic approach. Extensions to the setting where the interaction takes place on networks will be also discussed. Based on joint works with Sergey Nadtochiy.