| This thesis mainly studies some continuous insider trading models with market makers observing different structural information and also related filtering problem about a geometric Brownian motion.We investigate the existence and uniqueness of linear equilibrium for the considered insider trading models with financial significance and related mathematical problems.Firstly,we propose a continuous insider trading model under confidence pricing with multi-information observations,in which market makers not only know the total trading volume,but also some kind of relevant linear information about the risk asset when pricing the value of the risk asset in a semi-strong way.By applying filtering method and variational method,we obtain the optimal trading strategy of the insider,and find that there is no relation between the optimal trading strategy and the non-trivial confidence level of market makers.Secondly,we study the continuous insider trading model under pricing with some related information about a risk asset,in which market makers observe not only the total trading volume,but also some linear information about risk assets with related to noise trading.We obtain the optimal trading strategy and the maximum expected wealth of the insiderand find that the correlation degree of risk asset with noise trading affects the optimal trading strategy of the insider,that is,the more correlation degree of risk assets with noise trading,the less expected wealth of the insider,while if the risk asset value and noise trading volume are independent,the insider make the most expected wealth.Finally,we study a filtering problem about a geometric Brownian motion and obtain a dynamic equation of its best estimate filter.And by applying this filter equation,we solve an optimal problem of continuous insider trading when the risk asset satisfies some special geometric Brownian motion.It shows that the insider trading strength is gradually decreasing as insider trading approaches to deadline;however,because of the absolute advantage in information monopoly,the insider earns more profit as the trading time goes by. |
