The Research Of Pricing Privately Offered Fund Based On Utility

With the"asset management" era coming, the privately offered fund has become a significant force in China financial market. Compared with manual funds' incentive fee, the privately offered funds with option contracts and manager's own capital investing in the funds are more popular, and alleviate the moral hazard of the problems of information asymmetry. In this article, we price this fund based on utility indifference principal both in complete market and incomplete market. Assume that investors are risk-aversion, in order to maximize the investor's wealth utility combine with the optimal investment strategy and stochastic control principle, then allow to the principle of utility indifference, we get the partial differential equation which fund's price meet, and use the method of finite difference to solve the equation of price numerically. Then analyze the factors of the fund's price by the method of comparative static analysis. Besides, price the payoff of fund manager based on utility indifference principal, and analyze the risk-seeking behavior of the manager. Finally, we think of designing the incentive contract, we find the trade-off between fixed management fee and ex-performance fee, and give suggestions to the investors.The results show that:the utility indifference pricing of fund decreases contrarily as the risk-aversion increases; When risk aversion coefficient is large enough, the utility indifference price of the fund decreases contrarily as the maturity of the fund increases; The investors' attitudes towards risk affect the price only via the non-systematic risk of the fund:the weaker the correlation between fund and market is, the stronger the fund's non-systematic risk is, the attitude towards risk impose stronger influence on the fund's price, and vice versa, if they share completely correlation, non-systematic risk is zero, the attitude towards risk won't affect the price of the fund; When risk aversion coefficient is small enough, the utility indifference price increases as the volatility of fund increases, but when risk aversion coefficient is large enough, the utility indifference price decreases contrarily as the volatility of fund increases. Finally, from the perspective of the utility indifference price of manager's payoff, manager choose large or small volatility when he has large or small risk aversion coefficient, when the investor is risk-neutral, he may choose infinite volatility. We discuss the fund's contract design because of the trade-off between fixed management fee and ex-performance fee.