Optimal control of DC pension plan management under two incentive schemes. (English) Zbl 1411.91285

Summary: Since the late 1990s, a performance fee arrangement has been approved as a managerial incentive in direction contribution (DC) pension plan management to motivate managers. However, the fact that managers may take undue risk for the larger performance fees and thus reduce members’ utility has been a subject of debate. As such, this study investigates the optimal risk-taking policies of DC pension fund managers under both the single management fee scheme and a mixed scheme with a lower management fee, as well as an additional performance fee. The analytical solutions are derived by using the duality method and concavification techniques in a singular optimization problem. The results show the complex risk-taking structures of fund managers and recognize the win-win situation of implementing performance-based incentives in DC pension plan management. Under the setting of geometric Brownian motion asset price dynamics and constant relative risk aversion utility, the optimal risk investment proportion shows a peak-valley pattern under the mixed scheme. Further, the manager gambles for gain when fund wealth is low and time to maturity is short. As opposed to the existing literature, this study found that the risk-taking policy is more conservative when fund wealth is relatively large. Furthermore, the utilities of the manager and members could both be improved by appropriately choosing the performance fee rate.


91B30 Risk theory, insurance (MSC2010)
49N90 Applications of optimal control and differential games
Full Text: DOI


[1] Artzner, P.; Delbaen, F.; Eber, J.-M.; Heath., D. D., Coherent measures of risk, Mathematical Finance, 9, 203-28, (1999) · Zbl 0980.91042
[2] Bichuch, M.; Sturm., S., Portfolio optimization under convex incentive schemes, Finance and Stochastics, 18, 873-915, (2014) · Zbl 1360.91132
[3] Carpenter, J. N., Does option compensation increase managerial risk appetite?, Journal of Finance, 55, 2311-31, (2000)
[4] Cochrane, J. H., Asset pricing, (2005), Princeton: Princeton University Press, Princeton
[5] Elton, E. J.; Gruber, M. J.; Blake., C. R., Incentive fees and mutual funds, Journal of Finance, 58, 779-804, (2003)
[6] Fang, S.-C.; Xing, W.-X., Linear conic optimization, (2013), Beijing: Science Press, Beijing
[7] Foster, D. P.; Young., H. P., Gaming performance fees by portfolio managers, Quarterly Journal of Economics, 125, 1435-58, (2010) · Zbl 1209.91100
[8] Gerber, H. U.; Shiu., E. S. W., Geometric Brownian motion models for assets and liabilities: From pension funding to optimal dividends, North American Actuarial Journal, 7, 37-51, (2013)
[9] Gomez-Mejia, L.; Wiseman., R. M., Refraining executive compensation: An assessment and outlook, Journal of Management, 23, 291-374, (1997)
[10] Guan, G.-H.; Liang., Z.-X., Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework, Insurance: Mathematics and Economics, 57, 58-66, (2014) · Zbl 1304.91193
[11] Guan, G.-H.; Liang., Z.-X., A stochastic Nash equilibrium portfolio game between two DC pension funds, Insurance: Mathematics and Economics, 70, 237-44, (2016) · Zbl 1371.91156
[12] Guan, G.-H.; Liang., Z.-X., Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints, Insurance: Mathematics and Economics, 69, 224-37, (2016) · Zbl 1369.91197
[13] Han, N.-W.; Hung., M.-W., Optimal asset allocation for DC pension plans under inflation, Insurance: Mathematics and Economics, 51, 172-81, (2012) · Zbl 1284.91520
[14] Hawthorne, F., The dawning of performance fees, Institutional Investor, 20, 139-46, (1986)
[15] He, X.-D.; Kou., S., Profit sharing in hedge funds, Mathematical Finance, 28, 50-81, (2018) · Zbl 1403.91312
[16] Hodder, J. E.; Jackwerth., J. C., Incentive contracts and hedge fund management, Journal of Financial and Quantitative Analysis, 42, 811-26, (2007)
[17] Karatzas, I.; Lehoczky, J. P.; Shreve, S. E.; Xu., G.-L., Martingale and duality methods for utility maximization in incomplete markets, SIAM Journal on Control and Optimization, 29, 702-30, (1991) · Zbl 0733.93085
[18] Kwak, M.; Shin, Y. H.; Choi., U. J., Optimal investment and consumption decision of a family with life insurance, Insurance: Mathematics and Economics, 48, 176-88, (2011) · Zbl 1233.91150
[19] Li, C. W.; Tiwari., A., Incentive contract in delegated portfolio management, Review of Financial Studies, 22, 4681-714, (2009)
[20] Lin, H.-C.; Saunders, D.; Weng., C.-G., Optimal investment strategies for participating contracts, Insurance: Mathematics and Economics, 73, 137-55, (2017) · Zbl 1416.91205
[21] Merton, R. C., Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51, 247-57, (1969)
[22] Merton, R. C., Optimum consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3, 373-413, (1971) · Zbl 1011.91502
[23] Ngwira, B.; Gerrard., R., Stochastic pension fund control in the presence of poisson jumps, Insurance: Mathematics and Economics, 40, 283-92, (2007) · Zbl 1120.60063
[24] Pirvu, T. A.; Zhang., H.-Y., Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution, Insurance: Mathematics and Economics, 51, 303-9, (2012) · Zbl 1284.91529
[25] Stark, L. T., Performance incentive fees: An agency theoretic approach, Journal of Financial and Quantitative Analysis, 22, 17-32, (1987)
[26] Stoughton, N. M., Moral hazard and the portfolio management problem, Journal of Finance, 48, 2009-18, (1993)
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