Optimal Investment and Consumption with Fixed and Proportional Transaction Costs

2000 ◽  
Author(s):  
Hong Liu
Keyword(s):  
Transaction Costs ◽  
Optimal Investment ◽  
Proportional Transaction Costs ◽  
Optimal Investment And Consumption

scholarly journals Maximization of the long-term growth rate for a portfolio with fixed and proportional transaction costs

2008 ◽  
Vol 40 (03) ◽  
pp. 673-695 ◽  
Author(s):  
Takashi Tamura
Keyword(s):  
Transaction Costs ◽  
Impulsive Control ◽  
Optimal Growth ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Proportional Transaction Costs ◽  
Average Growth ◽  
Long Run ◽  
Riskless Asset

We study the problem of maximizing the long-run average growth of total wealth for a logarithmic utility function under the existence of fixed and proportional transaction costs. The market model consists of one riskless asset and d risky assets. Impulsive control theory is applied to this problem. We derive a quasivariational inequality (QVI) of ‘ergodic’ type and obtain a weak solution for the inequality. Using this solution, we obtain an optimal investment strategy to achieve the optimal growth.

MINIMIZING THE PROBABILITY OF LIFETIME RUIN: TWO RISKLESS ASSETS WITH TRANSACTION COSTS

2019 ◽  
Vol 49 (03) ◽  
pp. 847-883
Author(s):  
Xiaoqing Liang ◽  
Virginia R. Young
Keyword(s):  
Transaction Costs ◽  
Financial Market ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Money Market ◽  
The Other ◽  
Proportional Transaction Costs ◽  
Optimal Investment Strategy ◽  
The Individual ◽  
Riskless Asset

AbstractWe compute the optimal investment strategy for an individual who wishes to minimize her probability of lifetime ruin. The financial market in which she invests consists of two riskless assets. One riskless asset is a money market, and she consumes from that account. The other riskless asset is a bond that earns a higher interest rate than the money market, but buying and selling bonds are subject to proportional transaction costs. We consider the following three cases. (1) The individual is allowed to borrow from both riskless assets; ruin occurs if total imputed wealth reaches zero. Under the optimal strategy, the individual does not sell short the bond. However, she might wish to borrow from the money market to fund her consumption. Thus, in the next two cases, we seek to limit borrowing from that account. (2) We assume that the individual pays a higher rate to borrow than she earns on the money market. (3) The individual is not allowed to borrow from either asset; ruin occurs if both the money market and bond accounts reach zero wealth. We prove that the borrowing rate in case (2) acts as a parameter connecting the two seemingly unrelated cases (1) and (3).

scholarly journals Maximization of the long-term growth rate for a portfolio with fixed and proportional transaction costs

2008 ◽  
Vol 40 (3) ◽  
pp. 673-695 ◽  
Author(s):  
Takashi Tamura
Keyword(s):  
Transaction Costs ◽  
Impulsive Control ◽  
Optimal Growth ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Market Model ◽  
Proportional Transaction Costs ◽  
Average Growth ◽  
Long Run ◽  
Riskless Asset

We study the problem of maximizing the long-run average growth of total wealth for a logarithmic utility function under the existence of fixed and proportional transaction costs. The market model consists of one riskless asset and d risky assets. Impulsive control theory is applied to this problem. We derive a quasivariational inequality (QVI) of ‘ergodic’ type and obtain a weak solution for the inequality. Using this solution, we obtain an optimal investment strategy to achieve the optimal growth.

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