Continuous Insider Trading On Dynamic Assets Under Effects Of Partial Observations Or Correlated Noises

This paper mainly studies the filtering equations of two kinds of anticipative signal-observation systems and some applications in continuous insider trading.Firstly,for a class of nonlinear anticipative signal-observation systems whose initial signal value has a given correlation function with signal noise and observation noise,our method is based an enlargement of filtration technique to transform it into an adaptive signal-observation systems,and then obtain filtering equation.Secondly,for a class of nonlinear anticipative signal-observation systems with uncertain probability measure,we apply the enlargement of filtration method,Girsanov transform and minimax theorem to represent the systems as an adaptive signal-observation systems under a new probability measure,and then it obtains the filtering equation from the significance of this probability measure.Finally,for a class of continuous insider trading model with anticipative signal-observation systems,we apply filtering equation of anticipative signal-observation systems,and obtain the stochastic dynamic equation of price change under martingale pricing rule and the HJB equation which satisfies the value function of insider traders.