No-arbitrage determinant theorems on mean-reverting stock model in uncertain market

Stock model is used to describe the evolution of stock price in financial markets. Mean-reverting stock model in uncertain environment has been proposed to describe the stock price in long run. Arbitrage means that an investor can obtain profit without any risk, which does not exist in a complete market. This paper aims at proposing a sufficient condition as well as a necessary condition for an uncertain mean-reverting stock model being no-arbitrage. Besides, some examples are given to illustrate the usefulness of the no-arbitrage determinant theorem.