Presented by: 
Mr Patrick Laub (UQ)
Tue 14 Nov, 11:00 am - 12:00 pm
67-343 (Priestly Building)

Modern financers and insurers need to understand the risk they own in their portfolios, and to estimate the chance of a catastrophic loss or bankruptcy. Even with the most basic models (such as those of Black & Scholes or of Cramér & Lundberg) simple quantities such as quantiles are impossible to calculate directly. In my PhD, I have worked on density and Laplace transform approximation for the distribution of the sum of lognormals. Recently, with Pierre-Olivier Goffard, we have generalised the density approximation method (which relies on an orthogonal polynomial expansion) to general random sums. I'll outline the numerical aspects of the work, which includes quasi-Monte Carlo integration with importance sampling, and symbolic differentiation within Mathematica’s infinite precision algebra. The papers covered are available on my website
Patrick Laub is completing his PhD in applied probability at both UQ and Aarhus University, Denmark. Before this, he studied Software Engineering and Mathematics at UQ.


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