Uncertain contour process and its application in stock model with floating interest rate

Uncertain process is an important tool to model dynamic uncertain systems. This paper proposes a special type of uncertain processes, named contour processes, whose sample paths can be classified by their inverse uncertainty distributions. It is shown that the set of contour processes is closed under the extreme value operator and the time integral operator as well as the monotone function. As an application, this paper considers an uncertain stock model with floating interest rate, in which both the interest rate and the stock price follow uncertain differential equations. By means of contour processes, some pricing formulas are derived for the European options, American options and Asian options of the stock model.