Stochastic models for broker inventory in dealership markets with a cash management interpretation.
This paper investigates the problem of a broker in a dealership market whose buffer content (cash flow) is governed by a stochastic price-dependent demand and supply. The authors study three models. In the first model, buyers and sellers (borrowers and depositors) arrive independently in accordance with price-dependent compound Poisson streams. The second and the third models are two variants of diffusion approximations. For a certain natural revenue function, taking into account the trade-off between holding and shortage costs (opportunity loss and interest rates), they define relevant cost functionals and lay the groundwork for optimization purposes. The approach in analyzing and computing the cost functionals is based on the optional sampling theorem applied to a certain martingale.
scientific article; zbMATH DE number 2003990