On the average rate of return in a continuous time stochastic model

TL;DR

This paper extends the concept of average rate of return from discrete to continuous time stochastic models, proving its martingale property in a market modeled by multidimensional geometric Brownian motion.

Contribution

It introduces a continuous time definition of the average rate of return that satisfies economic postulates and proves its martingale property in a stochastic market model.

Findings

Defined the average rate of return for continuous models

Proved the martingale property of the average rate of return

Extended previous discrete models to continuous time

Abstract

In a discrete time stochastic model of a pension investment funds market Gajek and Kaluszka(2000a) have provided a definition of the average rate of return which satisfies a set of economic correctnes postulates. In this paper the average rate of return is defined for a continuous time stochastic model of the market. The prices of assets are modeled by the multidimensional geometrical Brownian motion. A martingale property of the average rate of return is proven.