European Option Pricing With Heterogeneous Beliefs And Logarithmic Utility

The economics under complete information always assume that investor knownthe assets'expected return and volatility.But in real world,the assets'expectedreturn is always unknown to us ,investor can but estimates it from past pricedata by hand ,i.e. incomplete information.Furthermore the estimation is a?ectedby investor's personal favoritism.So the information and personal favoritism theinvestor holden a?ected the assets'pricing ,then the option pricing.It showed thatit is more practical to make study of option pricing under incomplete information.Under incomplete information,literature [1] showed how the information'squality and personal favoritism the investor holden a?ect the expected utilitythrough build up a kind of act for economic person's mold,and derived the as-sets'equilibrium price and discount factor under CRRA(Constant Relative RiskAversion) utility function.On the base of it,literature [26],[27] introduced Euro-pean option pricing with logarithmic utility and power utility function which isadopted by the agent.But it is on the same assumption that the agents has thesame beliefs,i.e. they have the same estimate on the assets'expected return.Apparently,it is unreasonable that the agents have the same estimation on theassets'expected return.So the paper farther study the option pricing problem onthe conditions of the agents have heterogeneous beliefs and the utility function islogarithmic utility.On the agent economic model and according to the first welfaretheory this paper gained each equilibrium consumption ,furthermore,according tothe asset pricing theory this paper educed the assets'equilibrium price and discountfactor , obtained such conclusions that the assets'equilibrium price is una?ectedby investors'beliefs and the discount factor is equal to the weighted averaged of thevalues that in corresponding economics with homogeneous beliefs,then accordingto option pricing's current theory ,we gave the European option price formulas ondi?erent instances enumerated in the paper .At the end of the paper we ulteriorlythink about the market price of the default risk.