No arbitrage condition for positive diffusion price processes
At first, the authors present local martingale analysis. More exactly, they consider Markovian local martingale process \(X\) without drift and analyse when this process will reach the origin. For this purpose the construction of the weak solution by means of the method of time changes is used. Then with the help of the Ray-Knight theorem the necessary and sufficient condition for \(X\) to reach the origin is established. Afterwards, the equation is transformed and the criterion is stated when \(X\) is a genuine martingale. These results are used to solve the problem when a nonnegative diffusion process admits an equivalent martingale measure. So, the existence of an equivalent local martingale measure for the general Markovian stock price model is established.
scientific article; zbMATH DE number 2036993