Noise, risk premium, and bubble
The existence of the pricing kernel is shown to imply the existence of an ambient information process that generates market filtration. This information process consists of a signal component concerning the value of the random variable X that can be interpreted as the timing of future cash demand, and an independent noise component. The conditional expectation of the signal, in particular, determines the market risk premium vector. An addition to the signal of any term that is independent of X, which generates a drift in the noise, is shown to change the drifts of price processes in the physical measure, without affecting the current asset price levels. Such a drift in the noise term can induce anomalous price dynamics, and can be seen to explain the mechanism of observed phenomena of equity premium and financial bubbles.
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