Bayesian Inference via Filtering for a Class of Counting Processes: Application to the Micromovement of Asset Price

This paper highlights recent developments in a rich class of counting process models for the micromovement of asset price and in the Bayesian inference (estimation and model selection) via filtering for the class of models. A specific micromovement model built upon linear Brownian motion with jumping stochastic volatility is used to demonstrate the procedure to develop a micromovement model with specific tick-level sample characteristics. The model is further used to demonstrate the procedure to implement Bayes estimation via filtering, namely, to construct a recursive algorithm for computing the trade-by-trade Bayes parameter estimates, especially for the stochastic volatility. The consistency of the recursive algorithm model is proven. Simulation and real-data examples are provided as well as a brief example of Bayesian model selection via filtering.     

Optimal policy for an inventory system with backlogging and all-units discounts: Application to the composite lot size model

This paper examines an inventory model with full backlogging and all-units quantity discounts. The practical scenario of a salesperson offering compensation to a client so as not to lose the sale is considered. The cost of a backorder thus includes both a fixed cost and a further cost which is proportional to the length of time the said backorder exists. A first algorithm is developed to determine the optimal policy while some extensions to this algorithm are obtained that include additional conditions on the model. In particular, the well known composite lot size model, developed by Tersine, is solved, incorporating a new stockout cost and a new all-units discount. Numerical examples are provided to illustrate the application of the algorithms.