Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T09:05:16.507Z Has data issue: false hasContentIssue false
  • English
  • Français

MEAN–VARIANCE EQUILIBRIUM ASSET-LIABILITY MANAGEMENT STRATEGY WITH COINTEGRATED ASSETS

Part of: Mathematical finance Mathematical economics

Published online by Cambridge University Press:  06 November 2020

MEI CHOI CHIU Open the ORCID record for MEI CHOI CHIU [Opens in a new window]
MEI CHOI CHIU*
Affiliation:
Department of Mathematics and Information Technology, The Education University of Hong Kong, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates asset-liability management problems in a continuous-time economy. When the financial market consists of cointegrated risky assets, institutional investors attempt to make profit from the cointegration feature on the one hand, while on the other hand they need to maintain a stable surplus level, that is, the company’s wealth less its liability. Challenges occur when the liability is random and cannot be fully financed or hedged through the financial market. For mean–variance investors, an additional concern is the rational time-consistency issue, which ensures that a decision made in the future will not be restricted by the current surplus level. By putting all these factors together, this paper derives a closed-form feedback equilibrium control for time-consistent mean–variance asset-liability management problems with cointegrated risky assets. The solution is built upon the Hamilton–Jacobi–Bellman framework addressing time inconsistency.

Keywords

asset-liability managementcointegrationmean–variancetime inconsistency

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 91B70: Stochastic models
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 2 , April 2020 , pp. 209 - 234
Copyright
© Australian Mathematical Society 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alexander, C., “Optimal hedging using cointegration”, Phil. Trans. R. Soc. A 357 (1999) 2039–2058; doi:10.1098/rsta.1999.0416.CrossRefGoogle Scholar
Alexander, C., Giblin, I. and Weddington, W., “Cointegration and asset allocation: a new active hedge fund strategy”, Res. Int. Bus. Finance 16 (2002) 65–90; http://sro.sussex.ac.uk/id/eprint/40609/.Google Scholar
Baillie, R. and Bollerslev, T., “Common stochastic trends in a system of exchange rates”, J. Finance 44 (1989) 137–151; doi:10.1111/j.1540-6261.1989.tb02410.x. CrossRefGoogle Scholar
Basak, S. and Chabakauri, G., “Dynamic mean–variance asset allocation”, Rev. Financ. Stud. 23 (2010) 2970–3016; doi:10.2139/ssrn.965926. CrossRefGoogle Scholar
Bjork, T., Khapko, M. and Murgoc, A., “On time–inconsistent stochastic control in continuous time”, Finance Stoch. 21 (2017) 331–360; doi:10.1007/s00780-017-0327-5.CrossRefGoogle Scholar
Cerchi, M. and Havenner, A., “Cointegration and stock prices: the random walk on Wall Street revisited”, J. Econ. Dyn. Control 12 (2017) 333–346; doi:10.1016/0165-1889(88)90044-9.CrossRefGoogle Scholar
Chen, K. and Wong, H. Y., “Time-consistent mean–variance hedging of an illiquid asset with a cointegrated liquid asset”, Finance Res. Lett. 29 (2019) 184–192; doi:10.1016/j.frl.2018.07.004.CrossRefGoogle Scholar
Chiu, M. C., “Asset-liability management in continuous-time: cointegration and exponential utility”, in: Optimization and control for systems in the big-data era, Volume 252 of Int. Ser. Oper. Res. Manag. Sci. (Springer, Cham, 2017) 85–100; doi:10.1007/978-3-319-53518-0_6.CrossRefGoogle Scholar
Chiu, M. C. and Li, D., “Continuous-time mean-variance optimization of assets and liabilities”, Insur. Math. Econ. 39 (2006) 330–355; doi:10.1016/j.insmatheco.2006.03.006.CrossRefGoogle Scholar
Chiu, M. C. and Wong, H.Y., “Mean-variance portfolio selection of cointegrated assets”, J. Econ. Dyn. Control 35 (2011) 1369–1385; doi:10.1016/j.jedc.2011.04.003.CrossRefGoogle Scholar
Chiu, M. C. and Wong, H. Y., “Mean–variance asset-liability management: cointegrated assets and insurance liabilities”, Eur. J. Oper. Res. 223 (2012) 785–793; doi:10.1016/j.ejor.2012.07.009.CrossRefGoogle Scholar
Chiu, M. C. and Wong, H. Y., “Mean–variance principle of managing cointegrated risky assets and random liabilities”, Oper. Res. Lett. 41 (2013) 98–106; doi:10.1016/j.orl.2012.11.013.CrossRefGoogle Scholar
Chiu, M. C. and Wong, H. Y., “Dynamic cointegrated pairs trading: mean-variance time-consistent strategies”, J. Comput. Appl. Math. 290 (2015) 516–534; doi:10.1016/j.cam.2015.06.004.CrossRefGoogle Scholar
Chiu, M. C. and Wong, H. Y., “Robust dynamic pairs trading with cointegration”, Oper. Res. Lett. 46 (2018) 225–232; doi:10.1016/j.orl.2018.01.006.CrossRefGoogle Scholar
Chiu, M. C., Wong, H. Y. and Zhao, J., “Commodity derivatives pricing with cointegration and stochastic covariances”, Eur. J. Oper. Res. 246 (2015) 476–486; doi:10.1016/j.ejor.2015.05.012.CrossRefGoogle Scholar
Cui, X., Li, D., Wang, S. and Zhu, S., “Better than dynamic mean-variance: time inconsistency and free cash flow stream”, Math. Finance 22 (2012) 346–378; doi:10.1111/j.1467-9965.2010.00461.x.CrossRefGoogle Scholar
Duan, J. C. and Pliska, S. R., “Option valuation with co-integrated asset prices”, J. Econ. Dyn. Control 28 (2004) 727–754; doi:10.1016/S0165-1889(03)00042-3.CrossRefGoogle Scholar
Engle, R. and Granger, C., “Co-integration and error correction: representation, estimation and testing”, Econometrica 55 (1987) 251–276; doi:10.2307/1913236.CrossRefGoogle Scholar
Granger, C., “Some properties of time series data and their use in econometric model specification”, J. Econometrics 23 (1981) 121–130; doi:10.1016/0304-4076(81)90079-8.CrossRefGoogle Scholar
Hogan, S., Jarrow, R., Teo, M. and Warachkac, M., “Testing market efficiency using statistical arbitrage with applications to momentum and value strategies”, J. Financ. Econ. 73 (2004) 525–565; doi:10.1016/j.jfineco.2003.10.004.CrossRefGoogle Scholar
Hu, Y., Jin, H. and Zhou, X. Y., “Time-inconsistent stochastic linear–quadratic control”, SIAM J. Control Optim. 50 (2012) 1548–1572; doi:10.1137/110853960.CrossRefGoogle Scholar
Li, D. and Ng, W. L., “Optimal dynamic portfolio selection: multiperiod mean-variance formulation”, Math. Finance 10 (2000) 387–406; doi:10.1111/1467-9965.00100.CrossRefGoogle Scholar
Markowitz, H., “Portfolio selection”, J. Finance 7 (1952) 77–91; doi:10.1111/j.1540-6261.1952.tb01525.x.Google Scholar
Phillips, P. C. B., “Error correction and long-run equilibrium in continuous time”, Econometrica 59 (1991) 967–980; doi:10.2307/2938169.CrossRefGoogle Scholar
Taylor, M. and Tonks, M. I., “The internationalisation of stock markets and the abolition of U.K. exchange control”, Rev. Econ. Stat. 71 (1989) 332–336; doi:10.2307/1926980. CrossRefGoogle Scholar
Wei, J., Wong, K. C., Yam, S. C. P. and Yung, S. P., “Markowitz’s mean–variance asset-liability management with regime switching: a time-consistent approach”, Insur. Math. Econ. 53 (2013) 281–291; doi:10.1016/j.insmatheco.2013.05.008.CrossRefGoogle Scholar
Wong, T. W., Chiu, M. C. and Wong, H. Y., “Time-consistent mean-variance hedging of longevity risk: effect of cointegration”, Insur. Math. Econ. 56 (2014) 56–67; doi:10.1016/j.insmatheco.2014.03.001.CrossRefGoogle Scholar
Wong, T. W., Chiu, M. C. and Wong, H. Y., “Managing mortality risk with longevity bonds when mortality rates are cointegrated”, J. Risk Insur. 84 (2017) 987–1023; doi:10.1111/jori.12110.CrossRefGoogle Scholar
Yan, T. and Wong, H. Y., “Open-loop equilibrium strategy for mean-variance portfolio problem under stochastic volatility”, Automatica 107 (2019) 211–223; doi:10.2139/ssrn.3246173. CrossRefGoogle Scholar
Zhou, X. and Li, D., “Continuous-time mean-variance portfolio selection: a stochastic LQ framework”, Appl. Math. Optim. 42 (2000) 19–33; doi:10.1007/s002450010003.CrossRefGoogle Scholar