Stochastic modes for broker inventory in dealership markets with a cash management interpretation

We study the problem of a broker in a dealership market whose buffer conten t (cash flow) is governed by stochastic price-dependent demand and supply. Three model variants are considered. In the first model, buyers and sellers (borrowers and depositors) arrive independently in accordance with price-d ependent compound Poisson streams. The second and the third models are two variants of diffusion approximations. For a certain natural revenue functio n, taking into account the trade-off between holding and shortage costs (op portunity loss and interest rates), we define relevant cost functionals tha t lay the groundwork for optimization purposes. The approach in analyzing a nd computing the cost functionals is based on the optional sampling theorem applied to a certain martingale. (C) 2001 Elsevier Science B.V. All rights reserved.