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November 2009
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Welcome to the School of Mathematical Sciences

The University of Adelaide has a proud tradition of excellence in both teaching and research across the disciplines of Applied Mathematics, Pure Mathematics and Statistics.


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Ernest Oliver Tuck

Professor Ernest Oliver Tuck (1939–2009)

Donations to the Tuck Fellowship in honour of the late Ernie Tuck can be made using the Development and Alumni Donation Form.


 
Jim Denier
Head of School
Nigel Bean
Head of Applied Mathematics
Nicholas Buchdahl
Head of Pure Mathematics
Gary Glonek
Head of Statistics

Further information

Next event

Backward stochastic equations and equilibrium pricing in incomplete financial markets
15:10 Fri 27 Nov 09 | Macbeth Lecture Theatre | Professor Ulrich Horst | Humboldt-University, Berlin

Abstract...
The problem of equilibrium pricing in dynamically incomplete financial markets is one of the oldest problems in mathematical economics. The problem of equilibrium pricing is well understood for the benchmark case of complete markets where all risk factors can be hedged using the available assets. When markets are incomplete the situation is more involved, and to date no unified approach to incomplete markets is available. In this talk we review some recent results on equilibrium pricing in incomplete markets in discrete time when the market participants evaluate their risk exposures using dynamic risk measures. For such market situations we establish existence and uniqueness of equilibrium results and show that the problem of dynamic equilibrium pricing can be reduced to a recursive sequence of static one-period problems. When the flow of information is generated by independent random walks the equilibrium dynamics can be described by a coupled system of backward stochastic difference equations which renders our approach easily amenable to numerical simulations. We also comment on some of the mathematical challenges that currently prevent us from translating our results from discrete to continuous time, including the lack of existence and differentiability of solutions results for coupled systems of backward stochastic differential equations with non Lipschitz continuous drivers. The talk is based on joint work with Patrick Cheridito (Princeton University), Michael Kupper (Humboldt University) and Traian A. Pirvu (McMaster University)
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Recent news
ARC Grant successes
Congratulations to Tony Roberts, Charles Pearce, Robert Elliot, Andrew Metcalfe and all their collaborators on their success in the current round of ARC grants. The projects are "Development of innovative technologies for oil production based on the advanced theory of suspension flows in porous media" (Tony Roberts et al.), "Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems" (Charles Pearce et al.), "Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models" (Robert Elliott et al.) and "A new flood design methodology for a variable and changing climate" (Andrew Metcalfe et al.)