We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trial…
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8 results for “coin-tossing”
A novel likelihood function for MRFs approximates marginal likelihoods and uses copulas to reconstruct the joint likelihood.
problem Intractable partition function for MRF likelihoods.
method Approximate marginal likelihoods through a modified coin-tossing scenario, then reconstruct the joint likelihood using copulas.
result Our approach outperforms Laplace approximation and pseudolikelihood, especially as MRF size increases.
Develops a new measure for market efficiency based on informational-entropy.
problem Lack of a precise quantitative definition of market efficiency.
method Develops a measure based on informational-entropy.
result The new measure is equivalent to existing definitions of market efficiency.
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From t…
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 dep…
The Reality Gameq-fin.GN
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the `reality map', which rel…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
Constant Proportion Debt Obligations, Zeno's Paradox, and the Spectacular Financial Crisis of 2008q-fin.MF
CPDOs can't achieve a Cash-In event in finite tosses, mirroring Zeno's Paradox.
problem The impossibility of achieving a Cash-In event in CPDOs, mirroring Zeno's Paradox.
method Coin-tossing model and analysis of infinite geometric series.
result CPDOs can't achieve a Cash-In event in a finite lifetime, mirroring Zeno's Paradox.