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Multi-asset investment-consumption model with transaction costs. (English) Zbl 1137.91482

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.

MSC:

91B28 Finance etc. (MSC2000)
91B42 Consumer behavior, demand theory
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[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
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