The following seminars have been jointly organised by the Risk and Stochastics Group and the Department of Mathematics. The Seminar normally takes place on Thursdays from 12.00 - 13.00 in room NAB.1.09 (New Academic Building, LSE), unless stated below.
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. All are welcome to attend. ***If you are not an LSE member of staff or LSE student please email firstname.lastname@example.org with details of the Joint Risk and Stochastics and Financial Mathematics seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building***
Please contact the seminar administrator on email@example.com for further information about any of these seminars.
Tuesday 6 October - Nevroz Sen (McGill University)
***Change to usual day, time and venue***
17.30 - 18.30: Room 6.15 (Leverhulme Library), Columbia House (69 Aldwych),LSE
Estimation theory for non-linear major-minor mean field games
In the Mean Field Games (MFG) framework where there is an agent (so-called Major) which has asymptotically non vanishing influence on any other Minor agent, the best response control process of each Minor agent depends upon its own state, the Major agent's state and the conditional distribution of the generic minor agent, namely the system's stochastic mean field; this is in contrast to the basic MFG setup where the mean field is deterministic. The theory of MFG with a Major agent (MM-MFG) is well understood when the observations of the Minor agents are complete.
In this talk we analyze the non-linear MM-MFG problem where each Minor agent partially observes the Major agent's state. We employ non-linear filtering theory derived for McKean-Vlasov type state equations and the Separation Principle in order to analyze the game in the infinite population limit. The main results are the existence and uniqueness of the solutions to the stochastic MFG system equations and the epsilon-Nash equilibrium property where the best response control process of each Minor agent depends upon the conditional density generated by that agent's non-linear filter together with the system's mean field and its own state.
Joint work with Peter E. Caines
Thursday 8 October - Sebastian Herrmann (ETH Zürich)
Hedging with Small Uncertainty Aversion
We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security's cash gamma.
Thursday 22 October - Johannes Ruf (University College London and an Associate Member at the Oxford-Man Institute of Quantitative Finance)
Föllmer's Measure and Novikov/Kazamaki-Type Conditions
In the first part of the talk, I will discuss the construction of Föllmer's measure on the canonical path space. In the second part, I will discuss sharpened Novikov/Kazamaki-type conditions that provide sufficient and necessary conditions for the martingale property of a
nonnegative local martingale.
This talk is based on joined papers with Nicolas Perkowski and Martin Larsson.
Thursday 5 November - Yaroslav MeInyk (Swiss Financial Institute @ École polytechnique fédérale de Lausanne)
Title and abstract TBC
Thursday 19 November - Rémy Praz (Copenhagen Business School)
Equilibrium asset prcing with both liquid and illiquid markets
I study a general equilibrium model in which investors face endowment risk and trade two correlated assets; one asset is traded on a liquid market whereas the other is traded on an illiquid over-the-counter (OTC) market. Endowment shocks not only make prices drop, they also make the OTC asset more difficult to sell, creating an endogenous liquidity risk. This liquidity risk increases the risk premium of both the OTC asset and liquid asset. Furthermore, the OTC market frictions increase the trading volume and the cross-sectional dispersion of ownership in the liquid market. Finally, if the economy starts with only the OTC market, then I explain how opening a correlated liquid market can increase or decrease the OTC price depending on the illiquidity level. The model’s predictions can help explain several empirical findings.
Thursday 3 December - Kristoffer Glover (University of Technology, Sydney)
Title and abstract TBC