American Institute of Mathematical Sciences

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

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

 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.
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. 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. 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. 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. 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. 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. 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. doi: 10.1214/aoap/1177004966. Google Scholar

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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. 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. 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. 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. 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. 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. 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. doi: 10.1214/aoap/1177004966. Google Scholar
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