A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees

Taksar, Michael; Klass, Michael J.; Assaf, David

doi:10.1287/moor.13.2.277

Cited by 173 publications

(123 citation statements)

References 18 publications

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“…[2], [5], [8], [9], [11] . Of the recent contributions, [2] and [11] include transaction costs. [2] shows how the presence of a minimum cost per transaction gives rise to discrete optimal trading in random intervals, while [11] solves a two-asset capital growth problem with proportional transaction costs and proves that the optimal strategy is a control limit policy which confines the investor's portfolio to a certain wedgeshaped region by minimal (continuous) trading at the barriers .…”

Section: Introductionmentioning

confidence: 99%

“…(von Neumann-Morgenstern) or logc , that the investor's total discounted utility of consumption over an infinite horizon is maximised by a control limit investment policy, similar to the one in [11], and a consumption rate which depends on the state of the portfolio, at any time. The study draws inspiration from an early paper on the subject by Magill and Constantinides (see [9]), which contained the fundamental insight that the portfolio should be confined to a certain region of portfolio space with minimal effort.…”

Section: Introductionmentioning

confidence: 99%

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Portfolio Selection with Transaction Costs

Davis

Norman²

1990

Mathematics of OR

1,147

811

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This thesis considers an investor who can distribute wealth between two assets , one with deterministic rate of growth (eg. bank deposit account) , the other with growth governed by a Brownian motion with drift (eg. equity share) . Transfers between these holdings incur proportional transaction costs . The investor may consume continuously and costlessly from the bank , and requires a consumption and investment strategy which maximises total discounted utility of consumption over an infinite horizon .For a large class of utility functions , it is proved that maximum utility is achieved by a strategy-which confines the investor's portfolio to a certain wedge-shaped region in the portfolio plane, by minimal trading, and allows consumption at a rate depending at any time on the current state of the portfolio .Moreover it is shown that the optimal strategy does not lead to bankruptcy in finite time.The problem is treated rigorously as a reflected diffusion process, and the existence and uniqueness of the optimally-controlled wealth process are demonstrated.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Portfolio Selection with Transaction Costs

Davis

Norman²

1990

Mathematics of OR

1,147

811

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“…Proof: Let 3 be the conditionally log-optimum policy defined by (10) and (11). Let be any other admissible policy.…”

Section: Investment In Repeated Stochastic Horse Racesmentioning

confidence: 99%

“…The situation in discrete time markets is not as severe [10], but one can do substantially better by incorporating the costs into the model. Growth optimal investment in markets with costs was introduced by Taksar et al [11] in the context of geometric Wiener markets with one risky asset and cash. Several related works, notably Davis et al [9] and Akian et al [12], study investment policies that maximize the discounted utility of the consumption stream in markets with costs.…”

Section: Introductionmentioning

confidence: 99%

Growth optimal investment in horse race markets with costs

Iyengar

Cover

2000

IEEE Trans. Inform. Theory

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Abstract-We formulate the problem of growth optimal investment in horse race markets with proportional costs and study growth optimal strategies both for stochastic horse races as well as races where one does not make any distributional assumptions. Our results extend all known results for frictionless horse race markets to their natural analog in markets with costs.Index Terms-Growth optimality, proportional transaction costs, universal investment.

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“…[12] provide a numerical method to tackle the same problem in the general case with n stocks. The problem of maximizing the asymptotic return in the case of proportional transaction costs in the one-stock case is examined in [14]. The optimal investment strategy consists in keeping the fraction of wealth invested in the stock in a fixed interval [a, b].…”

Section: Introductionmentioning

confidence: 99%

A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets

Irle¹,

Prelle

2009

Statistics &Amp; Decisions

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional transaction costs. The performance of an investment strategy is measured by the average return of the corresponding portfolio over an infinite time horizon. At first, we derive a representation of the portfolio value process, which only depends on the relative fractions of the total portfolio value that the investor holds in the different stocks. This representation allows us to consider these so-called risky fractions as the decision variables of the investor. We show a certain kind of stationarity (Harris recurrence) for a quite flexible class of strategies (constant boundary strategies). Then, using renewal theoretic methods, we are able to describe the asymptotic return by the behaviour of the risky fractions in a "typical" period between two trades. Our results generalize those of [4], who considered a financial market model with one bond and one stock, to a market with a finite number n>1 of stocks. Terms of use: Documents inKeywords: Portfolio theory, transaction costs, Harris recurrence, renewal theory JEL classification: G11, C61 Claas Prelle AbstractWe consider a portfolio optimization problem in a Black-Scholes model with n stocks, in which an investor faces both fixed and proportional transaction costs. The performance of an investment strategy is measured by the average return of the corresponding portfolio over an infinite time horizon. At first, we derive a representation of the portfolio value process, whhich only depends on the relative fractions of the total portfolio value that the investor holds in the different stocks. This representation allows us to consider these so-called risky fractions as the decision variables of the investor. We show a certain kind of stationarity (Harris recurrence) for a quite flexible class of strategies (constant boundary strategies). Then, using renewal theoretic methods, we are able to describe the asymptotic return by the behaviour of the risky fractions in a "typical" period between two trades. Our results generalize those of [4], who considered a financial market model with one bond and one stock, to a market with a finite number n > 1 of stocks.

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A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees

Cited by 173 publications

References 18 publications

Portfolio Selection with Transaction Costs

Portfolio Selection with Transaction Costs

Growth optimal investment in horse race markets with costs

A renewal theoretic result in portfolio theory under transaction costs with multiple risky assets

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