***IN THE PLANNING STAGE***
Workshop on current challenges in financial mathematics and economics
Monday 24 August 2015 to Friday 28 August 2015
A week-long series of workshops
The recent (and on-going) financial crisis motivates a scrutinised study in the field of Financial Mathematics. In order to obtain better models, imperfections and complexity of real financial markets must be taken into account. Rather than assuming that arbitrary quantities of assets can be traded without impacting the market, liquidity effect needs to be carefully analysed. A representative list of interesting questions to study include:
a) How does individual investor's behaviour (e.g. posting buy/sell orders in electronic ex-changes) aggregate across the market to form liquidity?
b) In a financial system with highly interconnected banks, how does a single bank's liquidity shortage propagate to its counterparties and magnify to a system risk event?
On the other hand, rather than assuming that all market participants can be modelled by a representative agent, interaction among heterogeneous agents has became an important component to understand real markets. A considerable amount of e ort has been spent in understanding questions such as:
a) How does interaction between individuals manifest on a system level?
b) Do constrains on individual's actions reduce efficiency of the system?
Facing imperfections, good models must be robust, placing less emphasis on particular model assumptions which tend to be unrealistic in practical applications. Better understanding such issues is of strategic importance to maintain a healthy financial system, and are currently attracting considerable effect from researchers, industry practitioners, and also regulators.
To tackle financial modelling challenges as the ones described above, new mathematical tools are needed. To study liquidity effect, new results in queuing theory, self-excited point processes, and stochastic control theory have been developed. To model interacting agents, multi-dimensional backward stochastic di differential equations and mean-field games are actively studied. To obtain robust models, path-wise stochastic analysis has been enriched and martingale transport theory has been invented. Initial applications of these new mathematical tools are encouraging, and help to bring new insight and sometimes partial solutions to the aforementioned financial problems. However, the majority of the mathematical tools are still under development and their impact to a wide range of realistic financial problems still needs to be appreciated.
More information will be published soon. Please send any questions to Ian Marshall