Transaction costs in finance and inventory research

It is a well-known fact that inventory research has its roots in the monetary theory. In this note we sketch the interaction between inventory theory and finance today. We consider the development from a simple deterministic model to continuous-time stochastic models in modern finance. Hereby we restrict our study to consumption--investment problems incurring transaction costs which closely resembled decision problems in inventory control but differ in the modelling of uncertainty. Finally, we support the application of mathematical methods in finance to improve inventory models. Keywords: Consumption-investment problems; Transaction costs; Inventory models; Diffusion approximation