模糊厌恶下含汇率风险的最优投资策略
PDF下载 (3322)李 全,徐 松,王 伟.模糊厌恶下含汇率风险的最优投资策略[J].宁波大学学报(理工版),2021,34(2):102-108.DOI:
LI Quan,XU Song,WANG Wei.Optimal investment strategies with exchange rate risk and ambiguity aversion[J].Journal of Ningbo University(Natural Science & Engineering Edition),2021,34(2):102-108.DOI:
| Title: | Optimal investment strategies with exchange rate risk and ambiguity aversion |
| 作者: | 李 全, 徐 松, 王 伟 |
| Author(s): | LI Quan, XU Song, WANG Wei |
| 关键词: | 模糊厌恶; 汇率风险; 最优投资组合 |
| Keywords: | ambiguity aversion; exchange rate risk; optimal portfolio |
| 分类号: | O211.9 |
| 文献标识码: | A |
| 摘要: | 研究了模糊厌恶和指数效用情形下含汇率风险的稳健最优投资问题. 假定投资者是模糊厌恶且可投资无风险债券、国外股票和国内股票3种资产, 在最大化终端财富期望效用的目标下, 通过随机动态规划原理得到相应的HJB(Hamilton-Jacobi-Bellman)方程, 然后通过求解HJB方程和一阶最优条件得到模糊厌恶和模糊中性2种情形下最优投资策略的解析解, 最后给出数值结果和经济学解释. 结果表明, 模糊厌恶程度和汇率风险对最优投资策略影响较大. |
| Abstract: | The robust optimal investment problem with exchange rate risk is studied in the case of ambiguity aversion and exponential utility. We assume that investors are those of ambiguity aversion and plan on investing in risk-free bonds, foreign stocks and domestic stocks. With the goal of maximizing the expected utility of terminal wealth, the corresponding HJB equation is obtained using the principle of stochastic dynamic programming, and then the analytical solution of the optimal investment strategies with ambiguity aversion and ambiguity neutrality are obtained by using the first-order optimal conditions and solving the HJB equation. Finally, numerical results and economic explanations are given. The numerical results show that the degree of ambiguity aversion and exchange rate risk impose a great influence on the optimal investment strategies. |
| 参考文献 /References: | [1] 闫伟, 李树荣. 带有汇率因素的不连续价格过程的最优投资组合研究[J]. 运筹与管理, 2008, 17(3):134-139. [2] 费为银, 高贵云, 夏登峰. 考虑汇率变动的跨国直接投资和税收政策研究[J]. 系统工程学报, 2015, 30(6): 746-754; 864. [3] 费为银, 何丹丹, 张伟. 跳扩散下汇率变动的外商直接投资问题研究[J]. 系统工程理论与实践, 2015, 35(2): 283-290. [4] Guo C, Zhuo X Y, Constantinescu C, et al. Optimal reinsurance-investment strategy under risks of interest rate, exchange rate and inflation[J]. Methodology and Computing in Applied Probability, 2018, 20(4):1477-1502. [5] 黄婵, 王伟, 温利民. 汇率风险和方差保费原理准则下最优投资和再保险策略[J]. 应用概率统计, 2019, 35(5): 508-524. [6] 邢钰, 徐玉华, 王晓燕. 汇率带有跳跃情形下的外商直接投资的最优投资组合问题[J]. 数学的实践与认识, 2020, 50(9):284-295. [7] Ellsberg D. Risk, ambiguity, and the savage axioms[J]. The Quarterly Journal of Economics, 1961, 75(4):643-669. [8] Bossaerts P, Ghirardato P, Guarnaschelli S, et al. Ambiguity in asset markets: Theory and experiment[J]. The Review of Financial Studies, 2010, 23(4):1325-1359. [9] Dimmock S G, Kouwenberg R, Mitchell O S, et al. Ambiguity aversion and household portfolio choice puzzles: Empirical evidence[J]. Journal of Financial Economics, 2016, 119(3):559-577. [10] Maenhout P J. Robust portfolio rules and asset pricing[J]. Review of Financial Studies, 2004, 17(4):951-983. [11] Branger N, Larsen L S. Robust portfolio choice with uncertainty about jump and diffusion risk[J]. Journal of Banking & Finance, 2013, 37(12):5036-5047. [12] Zeng Y, Li D P, Chen Z, et al. Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility[J]. Journal of Economic Dynamics and Control, 2018, 88:70-103. [13] Sun Z Y, Zheng X X, Zhang X. Robust optimal investment and reinsurance of an insurer under variance premium principle and default risk[J]. Journal of Mathematical Analysis and Applications, 2017, 446(2): 1666-1686. [14] Zhang Q, Chen P. Robust optimal proportional reinsurance and investment strategy for an insurer with defaultable risks and jumps[J]. Journal of Computational and Applied Mathematics, 2019, 356:46-66. [15] Wang N, Zhang N, Jin Z, et al. Robust non-zero-sum investment and reinsurance game with default risk[J]. Insurance: Mathematics and Economics, 2019, 84:115- 132. |
| 备注/Memo: | 收稿日期: 2020－07－17. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 教育部人文社科基金（18YJC910012）; 浙江省教育厅科研项目（Y201430940）; 宁波市自然科学基金（202003N4144）. 第一作者: 李全（1996－）, 女, 贵州毕节人, 在读硕士研究生, 主要研究方向: 金融数学. E-mail: 2441237380@qq.com *通信作者: 王伟（1982－）, 男, 安徽安庆人, 博士/教授, 主要研究方向: 金融数学. E-mail: wangwei2@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
