834 research outputs found
A new formulation of asset trading games in continuous time with essential forcing of variation exponent
We introduce a new formulation of asset trading games in continuous time in
the framework of the game-theoretic probability established by Shafer and Vovk
(Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation,
the market moves continuously, but an investor trades in discrete times, which
can depend on the past path of the market. We prove that an investor can
essentially force that the asset price path behaves with the variation exponent
exactly equal to two. Our proof is based on embedding high-frequency
discrete-time games into the continuous-time game and the use of the Bayesian
strategy of Kumon, Takemura and Takeuchi (Stoch. Anal. Appl. 26 (2008)
1161--1180) for discrete-time coin-tossing games. We also show that the main
growth part of the investor's capital processes is clearly described by the
information quantities, which are derived from the Kullback--Leibler
information with respect to the empirical fluctuation of the asset price.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ188 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Kelly betting with quantum payoff: A continuous variable approach
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
Kelly Betting with Quantum Payoff: a continuous variable approach
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 her/his initial resources into coherent state amplitude.Comment: 14 pages, 8 figure
The Prediction Market for the Australian Football League
The purpose of this paper is to make a novel contribution to the literature on the prediction market for the Australian Football League, the major sports league in which Australian Rules Football is played. Taking advantage of a novel micro-level data set which includes detailed per-game player statistics, predictions are presented and tested out-of-sample for the simplest kind of bet: fixed odds win betting. It is shown that player-level statistics may be used to yield very modest profits net of transaction costs over a number of seasons, provided some more global variables are added to the model. A comparison of different specifications of the linear probability model (LPM) versus conditional logit (CLOGIT) regressions reveals that the LPM usually outperforms CLOGIT in terms of profitability. It is further shown that adding significant variables to a regression specification which is clearly superior in econometric terms may reduce the efficacy of the prediction and thus profits.
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