通胀风险下基于相对业绩的资产管理人的最优投资  

Optimal Investment for Asset Managers Based on Relative Performance with Inflation Risk

作　　者：董迎辉 魏思媛 殷子涵 王磊[1] DONG Yinghui;WEI Siyuan;YIN Zihan;WANG Lei(School of Mathematical Sciences,Suzhou University of Science and Technology,Suz)

机构地区：[1]苏州科技大学数学科学学院,苏州215009

出　　处：《工程数学学报》2023年第1期20-40,共21页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12071335);教育部人文社科基金(20YJAZH025)。

摘　　要：研究了资产管理人在考虑通胀风险和激励机制下的最优投资问题。考虑一个含通胀风险的连续时间模型的金融市场,资产管理人可投资于通胀指数债券、股票和无风险债券这三类资产。假设用相对业绩来评估资产管理人的业绩,其薪酬设为相对业绩的非线性函数。利用凹化技术和鞅方法得到了看涨期权型和看跌–看涨期权型两种不同方案下的最优相对业绩和最优投资策略的解析表达式,进一步对通胀风险和两种绩效机制下的模型参数对最优投资策略的影响进行了敏感性分析。发现通胀指数债券能够帮助投资人有效地对冲通胀风险,并且看涨–看跌期权型薪酬方案能改善经济不景气时的风险管理。An optimal investment problem is investigated under inflation risk and incentive schemes.Consider a continuous-time model of a financial market with inflation risk.Suppose that the financial market consists of three tradable assets:an index bond,a stock and a risk-free bond.The asset manager is remunerated through a scheme based on the performance of the fund with respect to a benchmark.A remuneration scheme is designed as a nonlinear function of the relative performance.The concavification technique and the martingale approach are applied to solve the optimization problem and the closed-form representations of the optimal relative performance and portfolio processes under two different remuneration schemes are derived.Furthermore,sensitivity analysis is presented to analyze the impacts of the two different incentive schemes and inflation risk on the optimal investment strategy of the asset manager.Numerical results reveal that inflation-indexed bonds can effectively help investors to hedge against inflation risk,and the call-put option compensation scheme can improve the risk management in bad economic states.

关 键 词：相对业绩 通胀风险 最优投资 凹化 

分 类 号：F832.48[经济管理—金融学]