Change of drift in one-dimensional diffusions
研究了一维扩散过程通过测度变换改变漂移的条件,给出了局部鞅成为真鞅的完整刻画,并应用于广义Heston模型的无套利分析。
Abstract It is generally understood that a given one-dimensional diffusion may be transformed by a Cameron–Martin–Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this, we have to know that the change-of-measure local martingale that we write down is a true martingale. We provide a complete characterisation of when this happens. This enables us to discuss the absence of arbitrage in a generalised Heston model including the case where the Feller condition for the volatility process is violated.