Optimal Consumption And Investment Problem With Perishable And Durable Consumer Goods Under Partial Information

Along with the development of economy and the improvement of living standards,people's consumption levels and investment concepts have gradually improved.More and more people are willing to invest funds into the financial field for getting more benefits.How to determine the amount of investment and consumption on the basis of existing wealth to achieve utility maximization is the optimal consumption and investment problem.The study of optimal consumption and investment problem has important theoretical and practical significance.Consumer goods are divided into perishable consumer goods and durable consumer goods according to the consumption characteristics of consumer good-s in use.For optimal consumption and investment problem with perishable and durable consumer goods,optimal consumption and investment strategies are obtained using the stochastic maximum principal and a backward separation technique under full and partial information,respectively.The main works are as follows:Firstly,optimal consumption and investment problem with perishable and durable consumer goods under full information is proposed.The investors can consume perishable consumer goods,assuming that the investors have three kinds of financial assets for an investment choice,risk-free assets,risky finance assets and durable consumer goods.The price models of the three assets are as-sumed to be the diffusion process with continuous time.The durable consumer goods are served as a risky finance asset,as the price model of durable consumer goods similar to the model of risky assets.Depreciation of durable consumer goods is also considered.Ito's formula is used to derive the wealth process,which is a stochastic differential equation with control contained in diffusion terms.Next,a general cost functional which makes objectives of investors achieve simultaneously is introduced.And then,the optimal consumption and investment problem with perishable and durable consumer goods under full information is presented,which is finding the optimal control subject to state equation in the set of admissible policies for minimum cost functional.Secondly,for optimal consumption and investment problem with perish-able and durable consumer goods under full information,the optimal consump-tion and investment strategy are solved by using the maximum principle method of stochastic systems.Meanwhile,a differential equation that looks like a Ric-cati equation is obtained.If the differential equation has a unique solution,the optimal control can be expressed as the feedback form of the state.At last,optimal consumption and investment problem with perishable and durable consumer goods under partial information is studied for only partial information can be observed in real life.A backward separation technology is used to deal with this problem.Optimal control is given by conjecturing,and then is proved.