Zhao, Xiao-Yan; Nie, Zan-Kan Multi-asset investment-consumption model with transaction costs. (English) Zbl 1137.91482 J. Math. Anal. Appl. 309, No. 1, 198-210 (2005). Summary: We consider the multi-asset optimal investment-consumption model: a riskless asset and \(d\) risky assets. when the initial time is \(t\geqslant 0\), for a proportional transaction costs and discount factors, we proof that the value function of the model is a unique viscosity solution of a Hamilton — Jacobi — Bellman (HJB) equations. Cited in 1 Document MSC: 91B28 Finance etc. (MSC2000) 91B42 Consumer behavior, demand theory Keywords:finance; investment-consumption and portfolio models; HJB equation; viscosity solution; transaction costs; discount factor PDFBibTeX XMLCite \textit{X.-Y. Zhao} and \textit{Z.-K. Nie}, J. Math. Anal. Appl. 309, No. 1, 198--210 (2005; Zbl 1137.91482) Full Text: DOI References: [1] Akian, M.; Menaldi, J. L.; Sulem, A., On an investment-consumption model with transaction costs, SIAM J. Control Optim., 34, 329-364 (1996) · Zbl 1035.91505 [2] Capuzzo-Dolcetta, I.; Lions, P.-L., Hamilton-Jacobi equations with state constraints, Trans. Amer. Math. Soc., 318, 543-683 (1990) · Zbl 0702.49019 [3] Crandall, M.; Ishii, H.; Lions, P.-L., User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27, 1-67 (1992) · Zbl 0755.35015 [4] Crandall, M.; Lions, P.-L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277, 1-42 (1983) · Zbl 0599.35024 [5] Davis, M. H.A.; Panas, V. G.; Zariphopoulou, T., European option pricing with transaction costs, SIAM J. Control Optim., 31, 470-493 (1993) · Zbl 0779.90011 [6] Fleming, W. H.; Soner, H. M., Controlled Markov Processes and Viscosity Solutions (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0773.60070 [7] Gikhman, I.; Skorohod, A., Stochastic Differential Equations (1972), Springer-Verlag: Springer-Verlag New York [8] Ishii, H.; Lions, P.-L., Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations, 83, 26-78 (1990) · Zbl 0708.35031 [9] Lions, P.-L., Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. 1: The dynamic programming principle and applications; 2: Viscosity solutions and uniqueness, Comm. Partial Differential Equations, 8, 1101-1174 (1983), 1229-1276 · Zbl 0716.49022 [10] Magill, M. J.P.; Constantinides, G. M., Portfolio selection with transaction costs, J. Econom. Theory, 13, 245-263 (1976) · Zbl 0361.90001 [11] Shreve, S. E.; Soner, H. M., Optimal investment and consumption with transaction costs, Ann. Appl. Probab., 4, 609-692 (1994) · Zbl 0813.60051 [12] Soner, H. M., Optimal control with state space constraints, SIAM J. Control Optim., 24, 552-562 (1986), 1110-1122 [13] Tourin, A.; Zariphopoulou, T., Numerical schemes for investment models with singular transactions, Comput. Econom., 7, 287-307 (1994) · Zbl 0824.90033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.