This paper studies an optimal portfolio-consumption choice with information cost. In financial market, investors collect market information to understand the market parameters,make reasonable investment and consumption choice while controlling risks, and finally gain utility. Information acquisition and portfolio-consumption choice are two important steps of investment behavior, which are a whole. Nevertheless, the existing literature usually only considers the cost of information acquisition or only considers portfolio-consumption choice. In order to study the overall behavior of investors in financial market, these two issues are considered together in this paper. Firstly, based on portfolio-consumption choice model in ambiguity market, a bilevel optimization problem is established to discuss how investors should acquire information and make investment-consumption strategies to maximize their comprehensive utilities. Then, the inner stochastic game problem with constraints is simplified into finding saddle point of a function, and the value function of game problem is provided via the function value at the saddle point, so that the objective function of the outer optimization problem can be represented as a non-convex and non-concave binary function. At last, the existence condition and the range of the optimal strategy are presented, and the sensitivity analysis is studied.
[1] Knight, F.: Risk, Uncertainty, and Profit. Houghton Miffin, New York (1921)
[2] Markowitz, H.: Porfolio selection. J. Financ. 7, 77-91(1952)
[3] Merton, R.C.: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econ. Stat. 51, 247-257(1969)
[4] Merton, R.C.: Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3(4), 373-413(1971)
[5] Karatzas, I., Lehoczky, J.P., Sethi, S.P., Shreve, S.E.: Explicit solution of a general consumption/investemnt problem. Math. Oper. Res. 11, 261-294(1986)
[6] Karatzas, I.: Optimization problem in the theory in continuous trading. SIAM J. Control. Optim. 27(6), 1221-1259(1989)
[7] Korn, R., Kraft, H.: A stochastic control approach to portfolio problems with stochastic interest rates. SIAM J. Control. Optim. 40(4), 1250-1269(2000)
[8] Zhou, X., Yin, G.: Markowitz’s mean-variance portfolio selection with regime switching: a continuous-time model. SIAM J. Control. Optim. 42(4), 1466-1482(2006)
[9] Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance. Springer, New York (1998)
[10] Bordigoni, G., Matoussi, A., Schweizer, M.: A stochastic control approach to a robust utility maximization problem. Stoch. Anal. Appl. 2, 125-151(2007)
[11] Hernández, D., Schied, A.: Robust utility maximization in a stochastic factor model. Stat. Decis. 24, 109-125(2006)
[12] Schied, A.: Robust optimal control for a consumption-investment problem. Math. Methods Oper. Res. 67, 1-20(2008)
[13] Bian, L.H., Li, X.Y., Li, Z.F.: Time-consistent investment strategies for a DC pension member with stochastic interest rate and stochastic income. J. Oper. Res. Soc. China (2022). https://doi.org/10.1007/s40305-021-00386-1
[14] Denis, L., Kervarec, M.: Optimal investment under model uncertainty in nondominated models. SIAM J. Control. Optim. 51(3), 1803-1822(2013)
[15] Epstein, L.G., Ji, S.: Ambiguous volatility, possibility and utility in continuous time. J. Math. Econ. 50(1), 269-282(2014)
[16] Matoussi, A., Possamai, D., Zhou, C.: Robust utility maximization in non-dominated models with 2BSDEs: the uncertain volatility model. Math. Financ. 25(2), 258-287(2015)
[17] Neufeld, A., Nutz, M.: Robust utility maximization with Lévy processes. Math. Financ. 28(1), 82-105(2018)
[18] Liang, Z., Ma, M.: Robust consumption-investment problem under CRRA and CARA utilities with time-varying confidence sets. Math. Financ. 30, 1035-1072(2020)
[19] Yang, Z., Liang, G., Zhou, C.: Constrained portofolio-consumption strategies with uncertain parameters and borrowing costs. Math. Financ. Econ. 3(3), 393-427(2019)
[20] Yang, Z., Lv, M., Wei, Z.: Optimal investment-consumption choice with portfolio constraint in ambiguity market. J. South China Normal Univ. (Nat. Sci. Ed.) 51(1), 94-97(2019)
[21] Liu, J., Chen, Z.P., Hui, Y.C.: Time consistent multi-period worst-case risk measure in robust portfolio selection. J. Oper. Res. Soc. China 6, 139-158(2018)
[22] Nieuwerburgh, S.V., Veldkamp, L.: Information acquisition and under-diversification. Rev. Econ. Stud. 77, 779-805(2010)
[23] Mele, A., Sangiorgi, F.: Uncertainty, information acquisition and price swings in asset markets. Rev. Econ. Stud. 82(4), 1533-1567(1982)
[24] French, K., Poterba, J.: Investor diversification and international equity markets. Am. Econ. Rev. 81, 222-226(1991)
[25] Van Nieuwerburgh, S., Veldkamp, L.: Information immobility and the home bias puzzle. J. Financ. 64, 1187-1215(2009)
[26] Kacperczyk, M., Sialm, C., Zheng, L.: On the industry concentration of actively managed equity mutual funds. J. Financ. 60, 1983-2011(2005)
[27] Jansen, J.: Information acquisition and strategic disclosure in oligopoly. J. Econ. Manag. Strategy 17(1), 113-148(2008)
[28] Hwang, H.S.: Optimal information acquisition for heterogenous duopoly firms. J. Econ. Theory 59(2), 385-402(1993)
