# American Institute of Mathematical Sciences

• Previous Article
A vendor-managed inventory model based on optimal retailers selection and reliability of supply chain
• JIMO Home
• This Issue
• Next Article
Human resources optimization with MARS and ANN: Innovation geolocation model for generation Z
doi: 10.3934/jimo.2022083
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## Optimal contracts and asset prices in a continuous-time delegated portfolio management problem

 1 School of Economics, Xihua University, 611139, Chengdu, China 2 School of Economic Mathematics, Southwestern University of Finance and Economics, 611130, Chengdu, China

*Corresponding author: Zheng Dou

Received  October 2019 Revised  January 2022 Early access May 2022

We study optimal contracts and asset prices in a financial market in which an investor delegates a portfolio manager to manage her wealth. The agency frictions are caused by the manager's "shirking" action and hidden effort. The shirking action converts part of the return of the managed portfolio into the manager's income without reducing his utility. The manager's effort improves the return of the portfolio but reduces the manager's utility. We illustrate this dynamic principal-agent problem under hidden effort and observable effort, respectively. When the effort is hidden, to alleviate the impact of moral hazard, the investor pays more for the manager's performance and always keeps the optimal contract related to the returns of the manager's portfolio and market portfolio, and their quadratic (co)variations. When the manager's effort is observable, the optimal contract is related to the return of the market portfolio if the agency friction caused by the shirking action is serious, but is only related to the return of the manager's portfolio if shirking is not serious. Analysing the expected utility of the manager, we find that he has a disposition to hide information about effort to pursue a higher expected utility.

Citation: Zheng Dou, Shaoyong Lai. Optimal contracts and asset prices in a continuous-time delegated portfolio management problem. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022083
##### References:
 [1] S. Basak and A. Pavlova, Asset prices and institutional investors, American Economic Review, 103 (2013), 1728-1758. [2] M. Brennan, Agency and asset pricing, working paper, 2008. Avialiable from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1104546. doi: 10.2139/ssrn.1104546. [3] A. Buffa, D. Vayanos and P. Wooley, Asset management contracts and equilibrium prices, Working paper, 2019. Available from: https://www.nber.org/system/files/working_papers/w20480/w20480.pdf. doi: 10.3386/w20480. [4] A. Cadenillas, J. Cvitanić and F. Zapatero, Optimal risk-sharing with effort and project choice, Journal of Economic Theory, 133 (2007), 403-440.  doi: 10.1016/j.jet.2005.12.007. [5] K. Chen, X. Wang, M. Huang and W. Ching, Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent, Journal of Industrial and Management Optimization, 14 (2018), 873-899.  doi: 10.3934/jimo.2018013. [6] D. Cuoco and R. Kaniel, Equilibrium prices in the presence of delegated portfolio management, Journal of Financial Economics, 101 (2011), 264-296.  doi: 10.1016/j.jfineco.2011.02.012. [7] J. Cvitanić and H. Xing, Asset pricing under optimal contracts, Journal of Economic Theory, 173 (2018), 142-180.  doi: 10.1016/j.jet.2017.10.005. [8] J. Cvitanić, D. Possamaï and N. Touzi, Dynamic programming approach to principal-agent problems, Finance and Stochastics, 22 (2018), 1-37.  doi: 10.1007/s00780-017-0344-4. [9] A. Capponi, J. Cvitanić and T. Yolcu, Optimal contracting with effort and misvaluation, Mathematics and Financial Economics, 7 (2013), 93-128.  doi: 10.1007/s11579-012-0088-z. [10] G. Carroll and D. Meng, Locally robust contracts for moral hazard, Journal of Mathematical Economics, 62 (2016), 36-51.  doi: 10.1016/j.jmateco.2015.11.001. [11] M. Fagart and C. Fluet, The first-order approach when the cost of effort is money, Journal of Mathematical Economics, 49 (2013), 7-16.  doi: 10.1016/j.jmateco.2012.09.002. [12] B. Holmstrom and P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica, 55 (1987), 303-328.  doi: 10.2307/1913238. [13] R. C. Leung, Dynamic contracts and the Sharpe ratio: Theory and evidence, Working paper, 2017. [14] A. Lioui and P. Poncet, Optimal benchmarking for active portfolio managers, European Journal of Operational Research, 226 (2013), 268-276.  doi: 10.1016/j.ejor.2012.10.043. [15] H. Ou-Yang, Optimal contracts in a continuous-time delegated portfolio management problem, Review of Financial Studies, 16 (2003), 173-208.  doi: 10.1093/rfs/16.1.0173. [16] Y. Sannikov, A continuous-time version of the principal-agent problem, Review of Economic Studies, 75 (2008), 957-984.  doi: 10.1111/j.1467-937X.2008.00486.x. [17] J. Sung and X. Wan, A general equilibrium model of a multifirm moral-hazard economy with financial markets, Mathematical Finance, 25 (2015), 827-868.  doi: 10.1111/mafi.12032. [18] X. Wang, Y. Lan and W. Tang, An uncertain wage contract model for risk-averse worker under bilateral moral hazard, Journal of Industrial and Management Optimization, 13 (2017), 1815-1840.  doi: 10.3934/jimo.2017020.

show all references

##### References:
 [1] S. Basak and A. Pavlova, Asset prices and institutional investors, American Economic Review, 103 (2013), 1728-1758. [2] M. Brennan, Agency and asset pricing, working paper, 2008. Avialiable from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1104546. doi: 10.2139/ssrn.1104546. [3] A. Buffa, D. Vayanos and P. Wooley, Asset management contracts and equilibrium prices, Working paper, 2019. Available from: https://www.nber.org/system/files/working_papers/w20480/w20480.pdf. doi: 10.3386/w20480. [4] A. Cadenillas, J. Cvitanić and F. Zapatero, Optimal risk-sharing with effort and project choice, Journal of Economic Theory, 133 (2007), 403-440.  doi: 10.1016/j.jet.2005.12.007. [5] K. Chen, X. Wang, M. Huang and W. Ching, Compensation plan, pricing and production decisions with inventory-dependent salvage value, and asymmetric risk-averse sales agent, Journal of Industrial and Management Optimization, 14 (2018), 873-899.  doi: 10.3934/jimo.2018013. [6] D. Cuoco and R. Kaniel, Equilibrium prices in the presence of delegated portfolio management, Journal of Financial Economics, 101 (2011), 264-296.  doi: 10.1016/j.jfineco.2011.02.012. [7] J. Cvitanić and H. Xing, Asset pricing under optimal contracts, Journal of Economic Theory, 173 (2018), 142-180.  doi: 10.1016/j.jet.2017.10.005. [8] J. Cvitanić, D. Possamaï and N. Touzi, Dynamic programming approach to principal-agent problems, Finance and Stochastics, 22 (2018), 1-37.  doi: 10.1007/s00780-017-0344-4. [9] A. Capponi, J. Cvitanić and T. Yolcu, Optimal contracting with effort and misvaluation, Mathematics and Financial Economics, 7 (2013), 93-128.  doi: 10.1007/s11579-012-0088-z. [10] G. Carroll and D. Meng, Locally robust contracts for moral hazard, Journal of Mathematical Economics, 62 (2016), 36-51.  doi: 10.1016/j.jmateco.2015.11.001. [11] M. Fagart and C. Fluet, The first-order approach when the cost of effort is money, Journal of Mathematical Economics, 49 (2013), 7-16.  doi: 10.1016/j.jmateco.2012.09.002. [12] B. Holmstrom and P. Milgrom, Aggregation and linearity in the provision of intertemporal incentives, Econometrica, 55 (1987), 303-328.  doi: 10.2307/1913238. [13] R. C. Leung, Dynamic contracts and the Sharpe ratio: Theory and evidence, Working paper, 2017. [14] A. Lioui and P. Poncet, Optimal benchmarking for active portfolio managers, European Journal of Operational Research, 226 (2013), 268-276.  doi: 10.1016/j.ejor.2012.10.043. [15] H. Ou-Yang, Optimal contracts in a continuous-time delegated portfolio management problem, Review of Financial Studies, 16 (2003), 173-208.  doi: 10.1093/rfs/16.1.0173. [16] Y. Sannikov, A continuous-time version of the principal-agent problem, Review of Economic Studies, 75 (2008), 957-984.  doi: 10.1111/j.1467-937X.2008.00486.x. [17] J. Sung and X. Wan, A general equilibrium model of a multifirm moral-hazard economy with financial markets, Mathematical Finance, 25 (2015), 827-868.  doi: 10.1111/mafi.12032. [18] X. Wang, Y. Lan and W. Tang, An uncertain wage contract model for risk-averse worker under bilateral moral hazard, Journal of Industrial and Management Optimization, 13 (2017), 1815-1840.  doi: 10.3934/jimo.2017020.
$\bar Z$ and $\bar Z^{obs}$
Sensitivity to the return of the market portfolio $U$ and $U^{obs}$
Expected excess returns. The excess return of stocks in large supply is in the top half of the graph, and the excess return of stocks in small supply is in the bottom half of the graph
The manager's expected utility
 [1] Chong Lai, Lishan Liu, Rui Li. The optimal solution to a principal-agent problem with unknown agent ability. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2579-2605. doi: 10.3934/jimo.2020084 [2] Yu Yuan, Hui Mi. Robust optimal asset-liability management with penalization on ambiguity. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021121 [3] Giulia Cavagnari, Antonio Marigonda, Benedetto Piccoli. Optimal synchronization problem for a multi-agent system. Networks and Heterogeneous Media, 2017, 12 (2) : 277-295. doi: 10.3934/nhm.2017012 [4] Xiulan Wang, Yanfei Lan, Wansheng Tang. An uncertain wage contract model for risk-averse worker under bilateral moral hazard. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1815-1840. doi: 10.3934/jimo.2017020 [5] Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial and Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1 [6] Jeongmin Han. Local Lipschitz regularity for functions satisfying a time-dependent dynamic programming principle. Communications on Pure and Applied Analysis, 2020, 19 (5) : 2617-2640. doi: 10.3934/cpaa.2020114 [7] Guy Barles, Ariela Briani, Emmanuel Trélat. Value function for regional control problems via dynamic programming and Pontryagin maximum principle. Mathematical Control and Related Fields, 2018, 8 (3&4) : 509-533. doi: 10.3934/mcrf.2018021 [8] Lihua Bian, Zhongfei Li, Haixiang Yao. Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1383-1410. doi: 10.3934/jimo.2020026 [9] Ryan Loxton, Qun Lin. Optimal fleet composition via dynamic programming and golden section search. Journal of Industrial and Management Optimization, 2011, 7 (4) : 875-890. doi: 10.3934/jimo.2011.7.875 [10] Mohammed Abdelghany, Amr B. Eltawil, Zakaria Yahia, Kazuhide Nakata. A hybrid variable neighbourhood search and dynamic programming approach for the nurse rostering problem. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2051-2072. doi: 10.3934/jimo.2020058 [11] Haiying Liu, Wenjie Bi, Kok Lay Teo, Naxing Liu. Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming. Journal of Industrial and Management Optimization, 2019, 15 (2) : 445-464. doi: 10.3934/jimo.2018050 [12] Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song, Yanping Ma. Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial and Management Optimization, 2018, 14 (2) : 653-671. doi: 10.3934/jimo.2017067 [13] Zutong Wang, Jiansheng Guo, Mingfa Zheng, Youshe Yang. A new approach for uncertain multiobjective programming problem based on $\mathcal{P}_{E}$ principle. Journal of Industrial and Management Optimization, 2015, 11 (1) : 13-26. doi: 10.3934/jimo.2015.11.13 [14] Amin Aalaei, Hamid Davoudpour. Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management. Journal of Industrial and Management Optimization, 2016, 12 (3) : 907-930. doi: 10.3934/jimo.2016.12.907 [15] Zhongbao Zhou, Ximei Zeng, Helu Xiao, Tiantian Ren, Wenbin Liu. Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1493-1515. doi: 10.3934/jimo.2018106 [16] Harald Held, Gabriela Martinez, Philipp Emanuel Stelzig. Stochastic programming approach for energy management in electric microgrids. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 241-267. doi: 10.3934/naco.2014.4.241 [17] Haibo Jin, Long Hai, Xiaoliang Tang. An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming. Journal of Industrial and Management Optimization, 2020, 16 (2) : 965-990. doi: 10.3934/jimo.2018188 [18] Hui Zhang, Jian-Feng Cai, Lizhi Cheng, Jubo Zhu. Strongly convex programming for exact matrix completion and robust principal component analysis. Inverse Problems and Imaging, 2012, 6 (2) : 357-372. doi: 10.3934/ipi.2012.6.357 [19] Jin Ma, Xinyang Wang, Jianfeng Zhang. Dynamic equilibrium limit order book model and optimal execution problem. Mathematical Control and Related Fields, 2015, 5 (3) : 557-583. doi: 10.3934/mcrf.2015.5.557 [20] Hoi Tin Kong, Qing Zhang. An optimal trading rule of a mean-reverting asset. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1403-1417. doi: 10.3934/dcdsb.2010.14.1403

2021 Impact Factor: 1.411