# Events/Seminars/SeminarLCU27062018Brigo

### From Thalesians

## Contents |

### Thalesians Seminar (London) — Damiano Brigo — Rogue traders with S-shaped utility vs VaR and expected shortfall.

**Damiano Brigo**

#### Date and Time

Wednesday, June 27, 2018, at 6:00 p.m.

#### Venue

Marriott Hotel, Canary Wharf London, UK

#### *Meetup.com*

You can register for this event and pay online on *Meetup.com*:
https://www.meetup.com/thalesians/events/251719407/

#### Abstract

We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players. We show that, in many standard market models, product design aimed at utility maximization is not constrained at all by VaR or ES bounds: the maximized utility corresponding to the optimal payoff is the same with or without ES constraints. By contrast we show that, in reasonable markets, risk management constraints based on a second more conventional concave utility function can reduce the maximum S-shaped utility that can be achieved by the investor, even if the constraining utility function is only rather modestly concave. It follows that product designs leading to unbounded S-shaped utilities will lead to unbounded negative expected constraining utilities when measured with such conventional utility functions. To prove these latter results we solve a general problem of optimizing an investor expected utility under risk management constraints where both investor and risk manager have conventional concave utility functions, but the investor has limited liability. We illustrate our results throughout with the example of the Black--Scholes option market. These results are particularly important given the historical role of VaR and that ES was endorsed by the Basel committee in 2012--2013.

#### Speaker

**Damiano Brigo** (born Venice, Italy 1966) is an applied mathematician and Chair in Mathematical Finance at Imperial College London. He is known for research in filtering theory and mathematical finance.

Brigo started his work with the development, with Bernard Hanzon and Francois Le Gland (1998), of the projection filters, a family of approximate nonlinear filters based on the differential geometry approach to statistics, also related to information geometry. With Fabio Mercurio (2002–2003), he has shown how to construct stochastic differential equations consistent with mixture models, applying this to volatility smile modeling in the context of local volatility models. With Aurelien Alfonsi (2005), Brigo introduced new families of multivariate distributions in statistics through the periodic copula function concept. Since 2002, Brigo contributed to credit derivatives modeling and counterparty risk valuation, showing with Pallavicini and Torresetti (2007) how data implied non-negligible probability that several names defaulted together, showing some large default clusters and a concrete risk of high losses in collateralized debt obligations prior to the financial crisis of 2007–2008. This work has been further updated in 2010 leading to a volume for Wiley, while a volume on the updated nonlinear theory of valuation, including credit effects, collateral modeling and funding costs, has appeared in 2013. Overall Brigo authored more than seventy publications and co-authored the book Interest rate models: theory and practice for Springer-Verlag, that quickly became an international reference for stochastic dynamic interest rate modeling in finance. Brigo has been the most cited author in the technical section of the industry influential Risk Magazine in 2006, 2010 and 2012.

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