For scalar SDEs with a one-sided reflection we study pathwise approximation, globally on a compact time interval or at a single time point. We consider algorithms based on sequential evaluations of the driving Brownian motion and establish upper and lower bounds for the minimal errors. Exploiting the relation to a reflected Ornstein-Uhlenbeck process, we also provide a new upper bound for a Cox-Ingersoll-Ross process.

Nowadays, high-speed computations are mandatory for financial and insurance institutes to survive in competition and to fulfill the regulatory reporting requirements that have just toughened over the last years. A majority of these computations are carried out on huge computing clusters, which are an ever increasing cost burden for the financial industry. There, state-of-the-art CPU and GPU architectures execute arithmetic operations with pre-defined precisions only, that may not meet the actual requirements for a specific application. Reconfigurable architectures like field programmable gate arrays (FPGAs) have a huge potential to accelerate financial simulations while consuming only very low energy by exploiting dedicated precisions in optimal ways. In this work we present a novel methodology to speed up multilevel Monte Carlo (MLMC) simulations on reconfigurable architectures. The idea is to aggressively lower the precisions for different parts of the algorithm without loosing any accuracy at the end. For this, we have developed a novel heuristic for selecting an appropriate precision at each stage of the simulation that can be executed with low costs at runtime. Further, we introduce a cost model for reconfigurable architectures and minimize the cost of our algorithm without changing the overall error. We consider the showcase of pricing Asian options in the Heston model. For this setup we improve one of the most advanced simulation methods by a factor of 3-9x on the same platform.