Before revision: A simple conjecture is presented concerning positive solutions of a scalar, time-varying, linear state equation with delay . Although the equation arises in the context of stock trading, no knowledge of finance is needed in the analysis to follow. Starting from positive initial conditions, the state X(k) is governed by a nonnegative constant parameter alpha and a time-varying parameter v(k) with known bounds but otherwise arbitrarily time-varying.
After revision: A simple conjecture is presented concerning positive solutions of a scalar, time-varying, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain \alpha and a sequence v(k) with known bounds but otherwise arbitrarily time-varying.