Parallel Simulations for Analysing Portfolios of Catastrophic Event Risk

At the heart of the analytical pipeline of a modern quantitative insurance/reinsurance company is a stochastic simulation technique for portfolio risk analysis and pricing process referred to as Aggregate Analysis. Support for the computation of risk measures including Probable Maximum Loss (PML) and the Tail Value at Risk (TVAR) for a variety of types of complex property catastrophe insurance contracts including Cat eXcess of Loss (XL), or Per-Occurrence XL, and Aggregate XL, and contracts that combine these measures is obtained in Aggregate Analysis. In this paper, we explore parallel methods for aggregate risk analysis. A parallel aggregate risk analysis algorithm and an engine based on the algorithm is proposed. This engine is implemented in C and OpenMP for multi-core CPUs and in C and CUDA for many-core GPUs. Performance analysis of the algorithm indicates that GPUs offer an alternative HPC solution for aggregate risk analysis that is cost effective. The optimised algorithm on the GPU performs a 1 million trial aggregate simulation with 1000 catastrophic events per trial on a typical exposure set and contract structure in just over 20 seconds which is approximately 15x times faster than the sequential counterpart. This can sufficiently support the real-time pricing scenario in which an underwriter analyses different contractual terms and pricing while discussing a deal with a client over the phone.Comment: Proceedings of the Workshop at the International Conference for High Performance Computing, Networking, Storage and Analysis (SC), 2012, 8 page

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure

Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model

We show that efficient simulations of the Kardar-Parisi-Zhang interface growth in 2 + 1 dimensions and of the 3-dimensional Kinetic Monte Carlo of thermally activated diffusion can be realized both on GPUs and modern CPUs. In this article we present results of different implementations on GPUs using CUDA and OpenCL and also on CPUs using OpenCL and MPI. We investigate the runtime and scaling behavior on different architectures to find optimal solutions for solving current simulation problems in the field of statistical physics and materials science.Comment: 14 pages, 8 figures, to be published in a forthcoming EPJST special issue on "Computer simulations on GPU