私募基金管理者的收益定价、风险选择与契约设计

黄冰华; $2

私募基金管理者的收益定价、风险选择与契约设计

引用本文：黄冰华，杨招军.私募基金管理者的收益定价、风险选择与契约设计[J].经济数学,2013,(1):60-66

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作者	单位
黄冰华，杨招军	(湖南大学金融与统计学院，湖南长沙 410079)

中文摘要:考虑到市场非完备和私募基金管理者风险厌恶的实际情形，本文根据效用无差别原理，得到基金管理者收益的确定性等价价值满足的偏微分方程，并运用有限差分法进行数值分析.结果表明：非系统风险溢价的增大使得收益价值与自有资金率呈递增但呈边际递减规律；管理者的风险选择决定于非系统风险和风险厌恶态度，在契约有限期的情形下，风险中性型管理者会选择无限大的基金波动率，风险厌恶程度低(高)的管理者会选择尽可能大(小)的基金波动率；并从确定性等价的角度讨论了契约设计问题.

中文关键词:随机控制 HJB方程私募基金确定性等价价值风险溢价

The Payoff’ Valuation and Risk Choice of Privately Offered Fund Manager and Contract Design

Abstract:Taking into account that markets are actually incomplete and managers are risk-averse, this paper obtained a partial differential equation satisfied by the certainty equivalent valuation of privately offered fund manager’s payoffs based on utility indifference principle, and we provided numerical solutions by finite difference methods. The results show that, the certainty equivalent valuation of privately offered fund manager’s payoff increases but decreases marginally with managerial ownership rate, which results from the increases of non-systematic risk premium; that manager’s risk choice relies on non-systematic risk and risk aversion attention; and that under the finite horizon of the contract, the risk-neutral manager would select infinite volatility, but the low (high) risk-aversion manager would select volatility as large (small) as possible. We also discussed contract design from a certainty equivalent perspective.

keywords:stochastic control HJB equation privately offered fund certainty equivalent valuation risk premium

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