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July  2016, 21(5): 1445-1454. doi: 10.3934/dcdsb.2016005

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

Min Dai 1, and  Zhou Yang 2,

1. 

Dept of Math and Center for Quantitative Finance, National University of Singapore
2. 

School of Mathematical Science, South China Normal University, Guangzhou, China

Received  October 2013 Revised  March 2014 Published  April 2016

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.
Keywords: regularity., transaction costs, finite horizon, Optimal investment and consumption.
Mathematics Subject Classification: Primary: 35k86, 35Q91; Secondary: 60H1.
Citation: Min Dai, Zhou Yang. A note on finite horizon optimal investment and consumption with transaction costs. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1445-1454. doi: 10.3934/dcdsb.2016005
References:
[1]

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.  Google Scholar

[2]

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.  Google Scholar

[3]

M. H. A. Davis and A. R. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research, 15 (1990), 676-713. doi: 10.1287/moor.15.4.676.  Google Scholar

[4]

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.  Google Scholar

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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.  Google Scholar

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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.  Google Scholar

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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.  Google Scholar

show all references

References:
[1]

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.  Google Scholar

[2]

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.  Google Scholar

[3]

M. H. A. Davis and A. R. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research, 15 (1990), 676-713. doi: 10.1287/moor.15.4.676.  Google Scholar

[4]

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.  Google Scholar

[5]

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.  Google Scholar

[6]

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.  Google Scholar

[7]

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.  Google Scholar

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