The Study Of The Risk Preference Model

In this paper ,we put forward the risk preference model whose prefer-ence modulus θis the elasticity index of the risk to the profit and thereexist a riskless securities in a price light.Then we calculate the model bytwo methods:one is to use K-T condition;the other is to use the ventureneutral probability.Comprasing with the past models,the certainty of indif-ference curve in Markowitz theory is resolved and calculation in practice isreduced,too.Meanwhile ,as the elasticity index of the risk to the profit , thepreference modulus θin this paper has more economic meaning.Then we discuss the e?ective frontier of the risk preference model re-stricted by a short sell,and give the decision condition of redundant securi-ties and ways and steps in resolving the risk preference model restricted bya short sell by eliminating the redundant securities.At last,we discuss the risk preference model in which there exist risk-less securities and a few inequality constraints.On one hand, we obtain aanalytic solution to the model under the particular circumstance ;on theother hand, the analytic solution is not worked out easily under the mostcircumstance.In general,we can use numerical method to calculate it.In thispaper,we use penalty function to work it out,which is more mature in the nu-merical implementation.And give the method and steps of compute process.