This paper introduces recent developments in the analysis of dynamic systems with partial observations applied to a specific model. The states of these systems are typically conditional distributions, which evolve in infinite dimensional spaces over time. Our analysis involves introducing unnormalized probabilities to transform nonlinear state transition equations to linear ones. With the linear equations, the existence of optimal feedback policies are proved for two models where demand and cash inventory are partially observed. In a third model where the current cash level (inventory) is not observed but a past level is fully observed, a sufficient statistic is provided to serve as a state. The last model serves as an example where a partially observed model has a finite dimensional state. In that model, we also establish the optimality of base-stock policies, hence generalizing corresponding classical models with full information.
About the speaker
Professor Alain Bensoussan is a leading academic mathematician and technology personality. He is a member of the French Academy of Sciences as well as a member of many other institutions board and academic journals. He led the INRIA of France (Institute National de la Recherche sur l’Informatique et l’Automatisme) bringing it to numerous technology research centers involving over 6,000 researchers. In addition Professor Bensoussan has been the Chairman and Chief Executive of the French Space Agency (CNES) as well as the European Space Agency (ESA). These in addition in hundreds of important contributions in dynamic systems mathematics and problems (including problems in Finance—American options and industrial applications).
* Following the presentation of Professor Bensoussan a discussion about future directions in Financial Engineering will follow |
