A Goal Seeking Investment Model

A probabilistic investment model is formulated as a Wiener process with a barrier. A planning horizon, targeted rate of return, discount rate, and the mean and variance rate of return are the important parameters in the model. Sensitivity analyses are studied. Several significant statements can be made: (1) contrary to traditional mean-variance portfolio models, rate of return variance may not always be an undesirable characteristic, since higher variance can increase the chances of achieving certain types of investment goals; (2) one can almost always achieve certain types of investment goals if the time horizon is sufficiently long.