Growth optimal investment in horse race markets with costs

Iyengar, Garud; Cover, Thomas M.

doi:10.1109/18.887881

Cited by 22 publications

(2 citation statements)

References 12 publications

(18 reference statements)

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“…The case of transaction costs is considered in Serva (1999), Cover and Iyengar (2000) and Aurell and Muratore-Ginanneschi (2002). Cases where the growth optimizer has access to a larger filtration is treated by for instance Ammendinger, Imkeller, and Schweizer (1998), who shows how expanding the set of available information increases the maximal growth rate.…”

Section: Notesmentioning

confidence: 99%

On the History of the Growth-Optimal Portfolio

Christensen

2012

Advances in Computer Science and Engineering: Texts

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The growth optimal portfolio (GOP) is a portfolio which has a maximal expected growth rate over any time horizon. As a consequence, this portfolio is sure to outperform any other significantly different strategy as the time horizon increases. This property in particular has fascinated many researchers in finance and mathematics created a huge and exciting literature on growth optimal investment. This paper attempts to provide a comprehensive survey of the literature and applications of the GOP. In particular, the heated debate of whether the GOP has a special place among portfolios in the asset allocation decision is reviewed as this still seem to be an area where some misconceptions exists. The survey also provides an extensive review of the recent use of the GOP as a pricing tool, in for instance the so-called "benchmark approach". This approach builds on the numéraire property of the GOP, that is, the fact that any other asset denominated in units of the GOP become a supermartingale

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Section: Notesmentioning

confidence: 99%

On the History of the Growth-Optimal Portfolio

Christensen

2012

Advances in Computer Science and Engineering: Texts

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“…markets with the property that at every time step one of the assets pays off and all the other assets pay nothing (the wealth invested is lost completely). Remarkably, horse-race markets are very special cases of general markets, being, in a sense, the extremal points of the distribution of asset returns [1,2]. As such they have been extensively investigated: they possess many of the usual attributes of financial markets but they also have the important additional property that each bet has a well defined end point at which its value becomes certain.…”

Section: Introductionmentioning

confidence: 99%

Kelly Betting with Quantum Payoff: a continuous variable approach

Tirone

Ghio

Livieri

et al. 2021

Quantum

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The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all their initial resources into coherent state amplitude.

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The von Neumann-Gale Growth Model and Its Stochastic Generalization

Evstigneev

Sc̣henk-Hoppé

Handbook on Optimal Growth 1

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Growth optimal investment in horse race markets with costs

Cited by 22 publications

References 12 publications

On the History of the Growth-Optimal Portfolio

On the History of the Growth-Optimal Portfolio

Kelly Betting with Quantum Payoff: a continuous variable approach

The von Neumann-Gale Growth Model and Its Stochastic Generalization

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