Asset price processes are completely described by information processes and investors' preferences. In this paper we derive the relationship between the process of investors' expectations of the terminal stock price and asset prices in a general continous time pricing kernel framework. To derive the asset price process we make use of the modern technique of forward-backward stochastic differential equations. With this approach it is possible to show the driving factors for stochastic volatility of asset prices and to give theoretical arguments for empirically well documented facts. We show that stylized facts that look at first hand like financial market anomalies may be explained by an information process with stochastic volatility.
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