scholarly journals Growth optimal investment in discrete-time markets with proportional transaction costs

2016 ◽  
Vol 48 ◽  
pp. 226-238
Author(s):  
N. Denizcan Vanli ◽  
Sait Tunc ◽  
Mehmet A. Donmez ◽  
Suleyman S. Kozat
Keyword(s):  
Transaction Costs ◽  
Discrete Time ◽  
Optimal Investment ◽  
Proportional Transaction Costs

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).

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics I: A Numerical Solution

2016 ◽  
Vol 06 (04) ◽  
pp. 1650018 ◽  
Author(s):  
Michal Czerwonko ◽  
Stylianos Perrakis
Keyword(s):  
Diffusion Process ◽  
Transaction Costs ◽  
Portfolio Selection ◽  
Discrete Time ◽  
Continuous Time ◽  
Jump Diffusion ◽  
Numerical Approach ◽  
Proportional Transaction Costs ◽  
Asset Portfolio ◽  
Time Formulation

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete-time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous-time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

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.

Hedging in discrete time under transaction costs and continuous-time limit

1999 ◽  
Vol 36 (1) ◽  
pp. 163-178 ◽  
Author(s):  
Pierre-F. Koehl ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Risky Asset ◽  
Market Model ◽  
Upper And Lower Bounds ◽  
Time Step ◽  
Proportional Transaction Costs ◽  
Call Options

We consider a discrete-time financial market model with L1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

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