No-arbitrage theorem for multi-factor uncertain stock model with floating interest rate
Published on Jun 1, 2017in Fuzzy Optimization and Decision Making4.13
· DOI :10.1007/s10700-016-9246-8
In the stock models, the prices of the stocks are usually described via some differential equations. So far, uncertain stock model with constant interest rate has been proposed, and a sufficient and necessary condition for it being no-arbitrage has also been derived. This paper considers the multiple risks in the interest rate market and stock market, and proposes a multi-factor uncertain stock model with floating interest rate. A no-arbitrage theorem is derived in the form of determinants, presenting a sufficient and necessary condition for the new stock model being no-arbitrage. In addition, a strategy for the arbitrage is provided when the condition is not satisfied.