In this paper, we propose an analytical stochastic dynamic programming (SDP) algorithm to address the optimal management problem of price-maker community energy storage. As a price-maker, energy storage smooths price differences, thus decreasing energy arbitrage value. However, this price-smoothing effect can result in significant external welfare changes by reducing consumer costs and producer revenues, which is not negligible for the community with energy storage systems. As such, we formulate community storage management as an SDP that aims to maximize both energy arbitrage and community welfare. To incorporate market interaction into the SDP format, we propose a framework that derives partial but sufficient market information to approximate impact of storage operations on market prices. Then we present an analytical SDP algorithm that does not require state discretization. Apart from computational efficiency, another advantage of the analytical algorithm is to guide energy storage to charge/discharge by directly comparing its current marginal value with expected future marginal value. Case studies indicate community-owned energy storage that maximizes both arbitrage and welfare value gains more benefits than storage that maximizes only arbitrage. The proposed algorithm ensures optimality and largely reduces the computational complexity of the standard SDP.