Probability and Finance: It's Only a Game!

By Glenn Shafer, Vladimir G Vovk. 2001

442 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ec8ae2b5ba90ec2ae5c2ea084fc60d663223db55

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Citations in the corpus

A tutorial on conformal prediction (2007, background): “Here are three equivalent conditions on the joint distribution of a sequence of random variables z1, . . . , zN , any of which can be taken as the definition of exchangeability.”
Stochastic processes in science, engineering, and finance (2006, background): “Hence, other stochastic models have been proposed for the price development of risky securities [12, 50, 64, 74].”
Insuring against loss of evidence in game-theoretic probability (2010, unknown): “Contents”
Good randomized sequential probability forecasting is always possible (2005, methodology): “3 of Shafer and Vovk (2001), which keeps his capital non-negative and makes him infinitely rich unless”
Competitive On‐line Statistics (2001, background): “; therefore, {Qθ | θ ∈ Θ} will be a “prequential statistical model” as discussed in [58] (for a fuller description of such “partially specified” probability distributions, see [51]).”
On the Regularities of Mass Random Phenomena (2012, background): “So, there is the algorithmic approach to randomness [9, 11] as well as the game-theoretic approach to randomness in finance [19].”
Information, Divergence and Risk for Binary Experiments (2009, background): “ y summarised in Appendix B. 7. For example: Nelson’s use of non-standard analysis (Nelson, 1987; Lutz and Musio, 2005) as the foundations for probability; Tops˝e’s (Tops˝e, 2006), Shafer and Vovk’s (Shafer and Vovk, 2001) game theory as a basis, and Le Cam’s use of Riesz measures on a vector lattic”
Estimating means of bounded random variables by betting (2020, background): “This process is a central object of study in the game-theoretic probability literature where it is referred to as the capital process [Shafer and Vovk, 2001].”
A comparison of global, recurrent and smoothed-piecewise neural models for Istanbul stock exchange (ISE) prediction (2005, methodology): “In general for a time series (TS) prediction problem, a predictor fits a model to given data and finds an approximate mapping function between the input and the output values (Shafer and Vovk, 2001; Petridis and Kehagias, 1998; Petridis et al., 2001).”
Weak and strong laws of large numbers for coherent lower previsions (2008, methodology): “Our choice is inspired by a combination of ideas discussed in (Shafer and Vovk, 2001, Lemma 3.3).”
Optimization Methods for Large-Scale Machine Learning (2016, background): “Such results reveals interesting connections between probability theory, machine learning, and game theory [137, 32].”
Probabilistic forecasts, calibration and sharpness (2007, background): “…probability forecasts for dichotomous events, rather than distributional forecasts of real-valued quantities, and they did not consider the problem that is tackled here, namely the comparative evaluation of competing forecasters, for which they hint at future work (Shafer and Vovk (2001), page 50).”
The Sources of Kolmogorov’s Grundbegriffe (2006, background): “Its philosophical ideas, especially Cournot’s principle, also remain powerful, even for those who want to go beyond the measuretheoretic framework (Shafer and Vovk, 2001).”