scholarly journals On the game interpretation of a shadow price process in utility maximization problems under transaction costs

2013 ◽  
Vol 17 (4) ◽  
pp. 819-838 ◽  
Author(s):  
Dmitry B. Rokhlin
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Shadow Price ◽  
Price Process

scholarly journals UTILITY MAXIMIZATION IN A BINOMIAL MODEL WITH TRANSACTION COSTS: A DUALITY APPROACH BASED ON THE SHADOW PRICE PROCESS

2014 ◽  
Vol 17 (04) ◽  
pp. 1450022 ◽  
Author(s):  
CHRISTIAN BAYER ◽  
BEZIRGEN VELIYEV
Keyword(s):  
Growth Rate ◽  
Asymptotic Expansion ◽  
Transaction Costs ◽  
Continuous Time ◽  
Shadow Price ◽  
Optimal Growth ◽  
Order Effect ◽  
Explicit Construction ◽  
Binomial Model ◽  
Price Process

We consider the problem of optimizing the expected logarithmic utility of the value of a portfolio in a binomial model with proportional transaction costs with a long time horizon. By duality methods, we can find expressions for the boundaries of the no-trade-region and the asymptotic optimal growth rate, which can be made explicit for small transaction costs (in the sense of an asymptotic expansion). Here we find that, contrary to the classical results in continuous time, see Janeček and Shreve (2004), Finance and Stochastics8, 181–206, the size of the no-trade-region as well as the asymptotic growth rate depend analytically on the level λ of transaction costs, implying a linear first-order effect of perturbations of (small) transaction costs, in contrast to effects of orders λ1/3 and λ2/3, respectively, as in continuous time models. Following the recent study by Gerhold et al. (2013), Finance and Stochastics17, 325–354, we obtain the asymptotic expansion by an almost explicit construction of the shadow price process.

scholarly journals Dual Formulation of the Utility Maximization Problem Under Transaction Costs

2001 ◽  
Vol 11 (4) ◽  
pp. 1353-1383 ◽  
Author(s):  
Griselda Deelstra ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Maximization Problem ◽  
Dual Formulation ◽  
Utility Maximization Problem

scholarly journals Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

2020 ◽  
Vol 45 (4) ◽  
pp. 1210-1236 ◽  
Author(s):  
Shuoqing Deng ◽  
Xiaolu Tan ◽  
Xiang Yu
Keyword(s):  
Dynamic Programming ◽  
Transaction Costs ◽  
Model Uncertainty ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Market Condition ◽  
Maximization Problem ◽  
Proportional Transaction Costs ◽  
Utility Indifference ◽  
Basic Features

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numéraire-based semistatic utility maximization problem with an exponential utility preference. The randomization techniques recently developed in Bouchard, Deng, and Tan [Bouchard B, Deng S, Tan X (2019) Super-replication with proportional transaction cost under model uncertainty. Math. Finance 29(3):837–860.], allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.], we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.] to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.

Utility Maximization Trading Two Futures with Transaction Costs

2013 ◽  
Vol 4 (1) ◽  
pp. 26-85 ◽  
Author(s):  
Maxim Bichuch ◽  
Steven Shreve
Keyword(s):  
Transaction Costs ◽  
Utility Maximization

Optimal exercise of American puts with transaction costs under utility maximization

2022 ◽  
Vol 415 ◽  
pp. 126684
Author(s):  
Xiaoping Lu ◽  
Dong Yan ◽  
Song-Ping Zhu
Keyword(s):  
Transaction Costs ◽  
Utility Maximization

Utility maximization on the real line under proportional transaction costs

2002 ◽  
Vol 6 (4) ◽  
pp. 495-516 ◽  
Author(s):  
Bruno Bouchard
Keyword(s):  
Transaction Costs ◽  
Real Line ◽  
Utility Maximization ◽  
Proportional Transaction Costs ◽  
The Real

Strong Innovation and its Applications to Information Diffusion Modelling in Finance

2002 ◽  
Vol 9 (2) ◽  
pp. 383-402
Author(s):  
T. Toronjadze
Keyword(s):  
Stock Price ◽  
Information Diffusion ◽  
Utility Maximization ◽  
Partial Information ◽  
Innovation Process ◽  
Full Information ◽  
Diffusion Modelling ◽  
Price Process ◽  
The Mean ◽  
Mean Variance

Abstract We consider the mean-variance hedging and utility maximization problems under partial information for diffusion models of the stock price process. The special feature of this paper is that we construct a strong innovation process for the stock price process which allows us to reduce the partial information case to the full information one.

Short Communication: A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios

2021 ◽  
Vol 12 (4) ◽  
pp. SC115-SC125
Author(s):  
Erhan Bayraktar ◽  
Christoph Czichowsky ◽  
Leonid Dolinskyi ◽  
Yan Dolinsky
Keyword(s):  
Transaction Costs ◽  
Utility Maximization ◽  
Short Communication ◽  
Optimal Portfolios ◽  
Proportional Transaction Costs
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