From approximate to exact probability models in dynamic portfolio decision theory

Abstract

In the academic literature dynamic portfolio theory under transaction cost literature is restricted to a continuous time framework which results in quasi-variational Hamilton-Jacobi-Bellman (HJB) free boundary Partial Differential Equations (PDEs). The objective of this article is to create a generic, robust, and efficient framework that could handle both discrete and continuous models simultaneously. The discrete time formulation is a special case of continuous time formulation. The article proposes probability deformation solution schemes and examines their efficiency. Analysis is restricted to the popular transaction cost frameworks introduced by Davis and Norman in 1990 and Taksar et al. in 1988. In contrast to continuous version of the model the discrete version of the model is intuitive and easy to implement. Easy to implement heuristics to solve dynamic portfolio problems are very valuable in providing insights in to re-balancing portfolios when faced with transaction costs.