## 数値解析セミナー

開催情報 火曜日　16:30～18:00　数理科学研究科棟(駒場) 056号室 齊藤宣一 http://www.infsup.jp/utnas/

### 2018年05月31日(木)

16:30-18:00   数理科学研究科棟(駒場) 056号室
Olivier Pironneau 氏 (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
[ 講演概要 ]
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.