The Research On Pricing Broker Collective Asset Management Scheme

The broker collective asset management scheme has become a significant forcein China financial market. In this article, we pricing this product based on utilityindifference principal. Assumed that incomplete market and investors arerisk-aversion, combined with the optimal investment strategy and stochastic controlprinciple, draw the HJB equation, then according to the principle of utilityindifference, we get the partial differential equation which product’s price meet, anduse the method of finite difference solve the equation of price numerically. The resultsshow that: when risk aversion coefficient is large enough, the utility indifferencepricing decreases contrarily as the product maturity date increases; The investors’attitudes towards risk affect the price via the non-systematic risk of the products: theweaker the correlation between products and market is, the stronger the products’non-systematic risk is, the risk attitudes impose stronger influence on the products’price, and vice versa, if they share completely correlation, non-systematic risk is zero,the risk attitude won’t affect the products’ prices to the slightest;. The price is linearto fixed management fee and excess fee. We also solve systematic and non-systematicrisk premium formula explicitly, and analyze the utility indifference pricing decreasescontrarily as the product volatile increases for the view of risk premium, which isbetray with the B-S conclusion. Finally, from the perspective of utility indifference,we discuss the product’ contract design because of the trade-off between fixedmanagement fee and ex-performance fee. The main contents are as follows:Firstly, we discuss the feature of product’ contract, and get payoff formula ofinvestors, presumed market is complete, investors allocate their wealth with threeasset in financial market, investors are expected to end moment wealth maximizationas the goal, select the optimal investment strategy, according to the principle of utilityindifference, using stochastic control method, derived the goods partial differentialequation satisfied the utility indifference, and according to the contract of brokerageset product, the corresponding boundary conditions are obtained.Secondly, discussed the brokerage set not under the co mplete market financialproducts pricing, because brokers set financial products trade is an asset and productmanagers are required to hold a part of fund share, the product not only systematicrisk, and shall not hedge unsystematic risk, in the same way, according to theprinciple of utility indifference, deduced the utility indifference pricing products satisfy partial differential equation.Finally, according to the value equation, we do the relevant economic analysisusing the finite difference method. Finally, from the prospective of the utilityindifference, we discuss the contract design problem of product.