Penalty methods for continuous-time portfolio selection with proportional transaction costs

2010 ◽  
Vol 13 (3) ◽  
pp. 1-31 ◽  
Author(s):  
Min Dai ◽  
Yifei Zhong
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Penalty Methods ◽  
Proportional Transaction Costs

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 SCALED AND STABLE MEAN-VARIANCE-EVAR PORTFOLIO SELECTION STRATEGY WITH PROPORTIONAL TRANSACTION COSTS

2017 ◽  
Vol 18 (4) ◽  
pp. 561-584 ◽  
Author(s):  
Ebenezer Fiifi Emire ATTA MILLS ◽  
Bo YU ◽  
Jie YU
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Downside Risk ◽  
Estimation Risk ◽  
Expected Return ◽  
Proportional Transaction Costs ◽  
Portfolio Returns ◽  
L2 Norm ◽  
The Mean ◽  
Mean Variance

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails.

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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