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A note on finite horizon optimal investment and consumption with transaction costs

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  • In this note, we remove the technical assumption $\gamma>0$ imposed by Dai et. al. [SIAM J. Control Optim., 48 (2009), pp. 1134-1154] who consider the optimal investment and consumption decision of a CRRA investor facing proportional transaction costs and finite time horizon. Moreover, we present an estimate on the resulting optimal consumption.
    Mathematics Subject Classification: Primary: 35k86, 35Q91; Secondary: 60H10.


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    M. Dai, L. Jiang, P. F. Li and F. H. Yi, Finite Horizon Optimal Investment and Consumption with Transaction Costs, SIAM Journal on Control and Optimization, 48 (2009), 1134-1154.doi: 10.1137/070703685.


    M. Dai and F. H. Yi, Finite horizon optimal investment with transaction costs: A paraoblic double obstacle problem, Journal of Differential Equations, 246 (2009), 1445-1469.doi: 10.1016/j.jde.2008.11.003.


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    H. Liu and M. Loewenstein, Optimal portfolio selection with transaction costs and finite horizons, Review of Financial Studies, 15 (2002), 805-835.doi: 10.1093/rfs/15.3.805.


    M. J. P. Magill and G. M. Constantinides, Portfolio selection with transaction costs, Journal of Economic Theory, 13 (1976), 264-271.doi: 10.1016/0022-0531(76)90018-1.


    R. C. Merton, Optimal consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3 (1971), 373-413.doi: 10.1016/0022-0531(71)90038-X.


    S. E. Shreve and H. M. Soner, Optimal investment and consumption with transaction costs, Annals of Applied Probability, 4 (1994), 609-692.doi: 10.1214/aoap/1177004966.

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