Wireless mobile network virtualization enables physical mobile network operators (PMNO) to partition their network resources into smaller slices and assign each slice to an individual virtual mobile network operator and then manages these virtual networks in a more dynamic and cost-effective fashion. How a PMNO allocates resources to individual slices while ensuring resource elasticity is a key issue. This paper presents a resource allocation algorithm in such a network virtualization scenario where resource considered here includes both sub-carriers and transmission power. The overall algorithm involves the following two major processes: firstly to virtualize a physical wireless network into multiple slices each representing a virtual network, where resources are allocated elastically based on traffic loads and channel state information during virtualization; secondly, to carry out physical resource allocation within each virtual network (or slice). In particular the paper adopts orthogonal frequency division multiplexing as its physical layer to achieve more efficient resource utilization. A multi-step dynamic optimization approach is proposed to achieve sub-carrier allocation using binary integer programming and power allocation using nonlinear programming. The aim is to achieve the following design goals: virtual network isolation, and resource efficiency. The simulation results show that the above goals have been achieved.