Applications of Discrete and Continuous Time Stochastic Control to the Models of Economic Dynamics and Finance

University Of Missouri-Columbia, Columbia MO

Investigators

Abstract

This research deals with new applications of discrete and continuous time stochastic control to the mathematical models of economic growth, mathematical finance and mathematical insurance, as well as developing novel non-traditional control techniques useful for this purpose. In the area of discrete time control, we will study and analyze convex-valued dynamical systems, similar to the ones used for the analysis of the mathematical models of economic growth and we will use these results in analysis of complex discrete time financial market models. In the second part of our research, we will study new applications of the optimal control of diffusion processes to optimization models in finance and insurance. We will investigate mixed regular-singular stochastic and impulse stochastic control appropriate for those problems. We also intend to study the class of nonlinear partial differential (or integral-differential) equations with gradient constraints that form an appropriate analytical framework for these models. The importance of these activities is in the development of new methodology of applications of stochastic control in mathematical finance and insurance. Successful completion of the research objectives will increase our understanding of the structure of the policy the financial and insurance optimization models and will allow one to get a better insight into the nature of the optimal dividend distribution policy to which a publicly traded financial corporation should adhere. More importantly, it will provide understanding of the risk control policy such an institution should follow.