This paper presents a runtime system for reconfigurable accelerators that supports elastic management: it enables effective sharing of accelerator resources across multiple applications. For each application, this runtime system allocates an appropriate amount of resources to satisfy its quality-of-service requirements, while minimising the overall execution time for a collection of applications. The effectiveness of this runtime system is due to a set of scheduling algorithms and strategies customised for different types of workloads. We demonstrate our approach by implementing a dynamic Monte Carlo bond options pricing design.