Investment-Reinvestment Problem with Stochastic Interest Rates: Model Development

It is the purpose of this article to introduce appropriate optimization teclmiques for solving investment and reinvestment problems with stochastic interest rates. An investment planning horizon ofN years is considered and it is assumed that the asset of the initial portfolio matures fully at or before the investment horizon. We assume that interest rates are eitherrandom variables with known or unknown distribution functions. An optimization teclmique for dealing with situations having random interest rates with unknown distribution functions is introduced. To deal with random interest rates with known distribution function a chance constraint programming (CCP) formulation of the problem is provided. A modifiedversion of the Hook and Jeeves pattern search for simulating the Equivalent Deterministic Form (EDF) of the CCP is introduced. By the fact that the iterative teclmique of Hook and Jeeves pattern search always requires an initial solution point to start its engine with, a teclmique for identifying an initial feasible solution which gives a solution as a lower bound to the optimum solution of the nonlinear EDF problem, is introduced

Keywords:

Investment- reinvestment , Stochastic programming , Simulation , Pattern Search , Linear Approximation