Using trading strategies to detect phase transitions in financial markets

Forrò, Zalàn; Woodard, Ryan; Sornette, Didier

doi:10.1103/physreve.91.042803

Cited by 5 publications

(2 citation statements)

References 35 publications

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“…Our scheme of the choice of strategy (game) is more adaptive than the scheme corresponding to the classical Parrondo game. The random strategies have already been considered in [23,24]. Actually, we should consider the Parrondo game as a toy model of portfolio optimization, as it ignores the cost of portfolio re-balancing.…”

Section: P N K a P N K B P N K A B P N K Gmentioning

confidence: 99%

The solution of Parrondo’s games with multi-step jumps

Saakian¹

2016

J. Stat. Mech.

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We consider the general case of Parrondo’s games, when there is a finite probability to stay in the current state as well as multi-step jumps. We introduce a modification of the model: the transition probabilities between different games depend on the choice of the game in the previous round. We calculate the rate of capital growth as well as the variance of the distribution, following large deviation theory. The modified model allows higher capital growth rates than in standard Parrondo games for the range of parameters considered in the key articles about these games, and positive capital growth is possible for a much wider regime of parameters of the model.

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Section: P N K a P N K B P N K A B P N K Gmentioning

confidence: 99%

The solution of Parrondo’s games with multi-step jumps

Saakian¹

2016

J. Stat. Mech.

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“…On average there is a motion due to the random switches between two potentials. The phenomenon is certainly related to portfolio optimization [16], [17]. In the related situation in economics, one is using the "volatility pumping" strategy in portfolio optimization, for two asset portfolios, keeping one half of the capital in the first asset, the other half in the second asset with high volatility [18].…”

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confidence: 99%

Exact probability distribution functions for Parrondo's games

2016

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We consider discrete time Brownian ratchet models: Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. We find that in some cases there are oscillations near the maximum of the probability distribution, and after many rounds there are two limiting distributions, for the odd and even total number of rounds of gambling. We assume that the solution of the aforementioned models can be applied to portfolio optimization.The Parrondo's games [1]- [8], related to the Brownian ratchets [9]-[15] are interesting phenomena at the intersection of game theory, econophysics and statistical physics, see [8] for the inter-disiplinary applications. In case of Brownian ratchets the particle moves in a potential, which randomly changes between 2 versions. For each there is a detailed balance condition. On average there is a motion due to the random switches between two potentials. The phenomenon is certainly related to portfolio optimization [16], [17]. In the related situation in economics, one is using the "volatility pumping" strategy in portfolio optimization, for two asset portfolios, keeping one half of the capital in the first asset, the other half in the second asset with high volatility [18].J. M. R. Parrondo invented his game following Brownian ratchets for the discrete time case [1], to model gambling. An agent uses two biased coins for the gambling, and both strategies are loosing. In some cases a random combination of two loosing games is a winning game. It is interesting that the opposite situation is also possible, a random combination of two winning games can give a loosing game.Parrondo's games have been considered either on the one dimensional axis with some periodic potential, or by looking at the time dependent version of the game parameters.For the first case the state of the system is characterized by the current value of the money X, and the choice of the strategy. There is a period M defining the rules, how capital X can move up or down. The rules of the game depend on Mod(X, M ), where M is the period of the "potential". Originally M = 3 games were considered, then M = 2 versions of Parrondo's games were constructed [7], [19]. For the history dependent versions of the game the current rules of the game depend on the past, whether there was a growth of capital in the previous rounds or not.Later many modifications of the games were invented, * Electronic address: saakian@yerphi.am i.e. different integers M for both games [20], the Allison mixture [21], where the random mixing of two random sequences creates some autocorrelation [22], and two envelope game problems [23]. Especially intriguing is the recent finding of a Parrondo's effect-like phenomenon in a Bayesian approach to the modelling of the work of a jury [24]: the unanimous decision of its members has a low confidence. All the mentioned works consider the situation with random walks, when there are random choices between differ...

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