We present a model for the optimal design of an online auction/store by a seller. The framework we use is a stochastic optimal control problem. In our setting, the seller wishes to maximize her average wealth level, where she can control her price per unit via her reputation level. The corresponding Hamilton-Jacobi-Bellmann equation is analyzed for an introductory case, and pulsing advertising strategies are recovered for resource allocation.

Paper is available on ArXiv at http://arxiv.org/pdf/1103.1918.pdf