Research On Several Portfolio Problems With Liabilities Under Inside Information

When the inside information appears in the financial market,the determined investment behavior based on the market information of investors.Therefore,these inside information will undoubtedly have a tremendous impact on the formulation of investment strategies.In the field of mathematical finance research,there are usually two kinds of mathematical tools for the study of this internal information.One of the key mathematical tools is the stochastic variational theory,and this paper mainly chooses another key technology to solve inside information problems,which is the enlargement of filtration technique.This paper mainly focuses on the wealth process,the objective function and expected utility maximization problems are all placed on the inside information market,and the portfolio strategy under the terminal liabilities and the inside information generated by the two different information flows are considered,the Several investor portfolio problems that the terminal liabilities of inside investors were proposed and solved.This paper mainly studies investigating portfolio issues with terminal liabilities under inside information,the details are as follows:Firstly,we study the optimal investment problem of stock price subject to the jump-diffusion process while the drift coefficient obeys the Ito process.The partial information model is processed by the enlargement of filtration technique.We apply a variant of the Kalman–Bucy filter to infer a signal,given a combination of an observation process and some additional information.This converts the combined partial and inside information model to a full information model,and the associated investment problem for HARA utility is explicitly solved via duality methods.Secondly,we studied a robust Markowitz mean-variance model with robustness.The payoffs of such claims cannot be predicted or hedged based on the underlying financial market even if the information of the financial market is increasingly available to the investor over time.The target of the investor is to minimize the variance in the worst scenario over all the possible realizations of the underlying intractable claim.Because of the time-inconsistent nature of the problem,both the standard penalization approach and the duality method used to tackle robust stochastic control problems fail in solving our problem.Instead,the quantile formulation approach is adopted to tackle the problem and an explicit closed-form solution is obtained.Third,we consider the problem of maximizing the expected utility of terminal wealth with a terminal random liability when the underlying asset price process is a continuous semimartingale.The optimal strategy is characterized in terms of a forward backward semimartingale system of equations.