Telescopes and Mathematical Finance

The European Southern Observatory (ESO) operates several astronomical telescopes. e.g, in the Atacama desert, Chile. One of the driest places on earth (picture).
Austria joined ESO in 2008. The Austrian Adaptive Optics Team (Indmath, RICAM and MathConsult, makers of UnRisk) is developing correction software to be used in the 40m extremely large telescope (E-ELT) that will be the largest ground-based telescope in 2020. It will have the size of a football stadium.

Its purpose: finding habitable planets. One problem: atmospheric turbulences blur images. Correction is carried out by deformable mirrors. Mathematical approach: In-the-loop-calibration.

Depending on the instrumentation, 7000 - 40.000 sensors shall detect irregularities in the incoming wavefront. The resulting system matrix of normal equations is dense and the system should be solved in a frequency of  500 Hz to 4 kHz .

Conventional matrix inversion software need specialized parallel hardware even for the smaller problem. The Cumulative Reconstructor of the Austrian Adaptive Optics team achieves a breathtaking speed-up of 1000.

Nice, but what has this to do with computational finance?

This are the similarities:

Astronomy and adaptive optics:
Data are changing rapidly due to turbulence, and only fast, stable and robust algorithms can meet the increasing real-time  requirements.
Computational finance:
Data are changing rapidly due to market movements. Fast, stable and robust algorithms lead to more reliable prices.

Astronomy and adaptive optics:
It is often difficult to distinguish between information and noise. An exoplanet is, if you are lucky, one pixel to be measured.
Computational finance:
Financial markets are per se erratic.

Astronomy and adaptive optics:
Different deep space objects need different methods for their detection and exploration. Multi conjugate, multi object, multi-sensor, multi method.
Computational finance:
Valuation and risk assessment gets more significant explanatory power by applying multi strategy, multi model, multi-method, multi scenario analysis.

Our numerical repertoire for valuations embraces Adaptive Integration (a asymptotic math method), Finite Elements with Streamline Diffusion, Fourier-based methods (linking with cos methods), all transferred from complex technical systems, and tuned and modified Monte Carlo schemes (including least square and  Longstaff Schwartz).

Embedded in a center focussing on inverse problems research, our calibration engines are blazingly fast and robust.

More details? Michael Aichinger and Andreas Binder will present selected results of their coming book A Workout in Computational Finance here.