Optimal investment and consumption under a continuous-time cointegration model with exponential utility

References

• Alexander, C., Optimal hedging using cointegration. Philos. Trans. R. Soc. London A: Math. Phys. Eng. Sci., 1999, 357(1758), 2039–2058. doi: 10.1098/rsta.1999.0416
   Web of Science ®Google Scholar
• Baillie, R.T. and Bollerslev, T., Common stochastic trends in a system of exchange rates. J. Financ., 1989, 44(1), 167–181. doi: 10.1111/j.1540-6261.1989.tb02410.x
   Web of Science ®Google Scholar
• Benth, F.E. and Karlsen, K.H., A note on merton's portfolio selection problem for the schwartz mean-reversion model. Stoch. Anal. Appl., 2005, 23(4), 687–704. doi: 10.1081/SAP-200064457
   Web of Science ®Google Scholar
• Brennan, M.J., Schwartz, E.S. and Lagnado, R., Strategic asset allocation. J. Econ. Dyn. Control, 1997, 21(8), 1377–1403. doi: 10.1016/S0165-1889(97)00031-6
   Web of Science ®Google Scholar
• Campbell, J.Y., Stock return and the term structure. J. Financ. Econ., 1987, 18, 373–399. doi: 10.1016/0304-405X(87)90045-6
   Web of Science ®Google Scholar
• Campbell, J.Y. and Shiller, R.J., The dividend-price ratio and expectations of future dividends and discount factors. Rev. Financ. Stud., 1988, 1(3), 195–228. doi: 10.1093/rfs/1.3.195
   Web of Science ®Google Scholar
• Cerchi, M. and Havenner, A., Cointegration and stock prices: The random walk on wall street revisited. J. Econ. Dyn. Control, 1988, 12(2–3), 333–346. doi: 10.1016/0165-1889(88)90044-9
   Web of Science ®Google Scholar
• Chen, Y., Dai, M. and Zhao, K., Finite horizon optimal investment and consumption with cara utility and proportional transaction costs. In Stochastic Analysis and Applications to Finance: Essays in Honour of Jia-an Yan, pp. 39–54, 2012 (World Scientific).
   Google Scholar
• Chiu, M.C. and Wong, H.Y., Mean–variance portfolio selection of cointegrated assets. J. Econ. Dyn. Control, 2011, 35(8), 1369–1385. doi: 10.1016/j.jedc.2011.04.003
   Web of Science ®Google Scholar
• Chiu, M.C. and Wong, H.Y., Mean–variance asset–liability management: Cointegrated assets and insurance liability. Eur. J. Oper. Res., 2012, 223(3), 785–793. doi: 10.1016/j.ejor.2012.07.009
   Web of Science ®Google Scholar
• Chiu, M.C. and Wong, H.Y., Mean-variance principle of managing cointegrated risky assets and random liabilities. Oper. Res. Lett., 2013a, 41(1), 98–106. doi: 10.1016/j.orl.2012.11.013
   Web of Science ®Google Scholar
• Chiu, M.C. and Wong, H.Y., Optimal investment for an insurer with cointegrated assets: Crra utility. Ins.: Math. Econ., 2013b, 52(1), 52–64.
   Web of Science ®Google Scholar
• Duan, J.-C. and Pliska, S.R., Option valuation with co-integrated asset prices. J. Econ. Dyn. Control, 2004, 28(4), 727–754. doi: 10.1016/S0165-1889(03)00042-3
   Web of Science ®Google Scholar
• Engle, R.F. and Granger, C.W., Co-integration and error correction: Representation, estimation, and testing. Econometrica, 1987, 55(2), 251–276. doi: 10.2307/1913236
   Web of Science ®Google Scholar
• Fama, E.F. and French, K.R., Permanent and temporary components of stock prices. J. Political Econ., 1988, 96(2), 246–273. doi: 10.1086/261535
   Web of Science ®Google Scholar
• Fleming, W.H. and Soner, H.M., Controlled Markov Processes and Viscosity Solutions, volume 25, 2006 (Springer Science & Business Media: New York).
   Google Scholar
• Granger, C.W., Some properties of time series data and their use in econometric model specification. J. Econom., 1981, 16(1), 121–130. doi: 10.1016/0304-4076(81)90079-8
   Web of Science ®Google Scholar
• Kim, T.S. and Omberg, E., Dynamic nonmyopic portfolio behavior. Rev. Financ. Stud., 1996, 9(1), 141–161. doi: 10.1093/rfs/9.1.141
   Web of Science ®Google Scholar
• Korn, R. and Kraft, H., On the stability of continuous-time portfolio problems with stochastic opportunity set. Math. Financ., 2004, 14(3), 403–414. doi: 10.1111/j.0960-1627.2004.00197.x
   Web of Science ®Google Scholar
• Lee, S. and Papanicolaou, A., Pairs trading of two assets with uncertainty in co-integration's level of mean reversion. Int. J. Theor. Appl. Financ., 2016, 19(08), 1650054. doi: 10.1142/S0219024916500540
   Google Scholar
• Lim, T. and Quenez, M.-C., et al., Exponential utility maximization in an incomplete market with defaults. Electron. J. Probab., 2011, 16, 1434–1464. doi: 10.1214/EJP.v16-918
   Web of Science ®Google Scholar
• Liu, J., Portfolio selection in stochastic environments. Rev. Financ. Stud., 2007, 20(1), 1–39. doi: 10.1093/rfs/hhl001
   Web of Science ®Google Scholar
• Markowitz, H., Portfolio selection. J. Financ., 1952, 7(1), 77–91.
   Web of Science ®Google Scholar
• Merton, R.C., Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat., 1969, 51(3), 247–257. doi: 10.2307/1926560
   Web of Science ®Google Scholar
• Merton, R.C., Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory, 1971, 3(4), 373–413. doi: 10.1016/0022-0531(71)90038-X
   Web of Science ®Google Scholar
• Mudchanatongsuk, S., Primbs, J.A. and Wong, W., Optimal pairs trading: A stochastic control approach. In American Control Conference, 2008, pp. 1035–1039, 2008 (IEEE).
   Google Scholar
• Øksendal, B., Stochastic Differential Equations: An Introduction with Applications, 2003 (Springer: Berlin).
   Google Scholar
• Samuelson, P.A., Lifetime portfolio selection by dynamic stochastic programming. Rev. Econ. Stat., 1969, 51(3), 239–246. doi: 10.2307/1926559
   Web of Science ®Google Scholar
• Serletis, A., A cointegration analysis of petroleum futures prices. Energy Econ., 1994, 16(2), 93–97. doi: 10.1016/0140-9883(94)90002-7
   Web of Science ®Google Scholar
• Shen, Y. and Siu, T.K., Optimal investment and consumption in a continuous-time co-integration model. IMA J. Manage. Math., 2017, 28(4), 501–530.
   Web of Science ®Google Scholar
• Taylor, M.P. and Tonks, I., The internationalisation of stock markets and the abolition of uk exchange control. Rev. Econ. Stat., 1989, 71(2), 332–336. doi: 10.2307/1926980
   Web of Science ®Google Scholar
• Tourin, A. and Yan, R., Dynamic pairs trading using the stochastic control approach. J. Econ. Dyn. Control, 2013, 37(10), 1972–1981. doi: 10.1016/j.jedc.2013.05.010
   Web of Science ®Google Scholar
• Wachter, J.A., Portfolio and consumption decisions under mean-reverting returns: An exact solution for complete markets. J. Financ. Quan. Anal., 2002, 37(01), 63–91. doi: 10.2307/3594995
   Web of Science ®Google Scholar
• Xia, Y., Learning about predictability: The effects of parameter uncertainty on dynamic asset allocation. J. Financ., 2001, 56(1), 205–246. doi: 10.1111/0022-1082.00323
   Web of Science ®Google Scholar
• Yong, J. and Zhou, X.Y., Stochastic Controls: Hamiltonian Systems and HJB Equations, volume 43, 1999 (Springer Science & Business Media: New York).
   Google Scholar
• Zhu, S.-P. and Ma, G., An analytical solution for the HJB equation arising from the merton problem. Int. J. Financ. Eng., 2018, 5(01), 1850008. doi: 10.1142/S2424786318500081
   Google Scholar