I agree with your post. Mathematics is just a tool. The reality of financial markets is that it's impossible to incorporate all the variables. Just do a search in Google Scholar for tensor analysis of financial markets and the problems inherent in analyzing financial markets becomes apparent.
The post below appeared on Medium. The author gives some good guidance as to how we should be looking at financial markets and the models we build around them.
Mathematics is never out of the picture - but must be tooled to suit the problem. Quantum mechanics is a classic example where probability theory replaced classical mathematics to describe the quantum world. In financial markets, there are limits as to what we can know at any one point in time regardless how much data we analyze. It's the nature of the beast.
The Trinity Of Errors In Financial Models: An Introductory Analysis Using TensorFlow Probability
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Finance is not a precise predictive science like physics. Not even close. So let’s not treat academic theories and models of finance as if they were models of quantum physics.
All financial models, whether based on academic theories or data mining strategies, are at the mercy of the trinity of modeling errors. While this trifecta of errors can be mitigated with appropriate modeling tools, it cannot be eliminated. There will always be asymmetry of information and cognitive biases. Models of asset values and risks will change over time due to the dynamic nature of capitalism, human behavior, and technological innovation."
The post below appeared on Medium. The author gives some good guidance as to how we should be looking at financial markets and the models we build around them.
Mathematics is never out of the picture - but must be tooled to suit the problem. Quantum mechanics is a classic example where probability theory replaced classical mathematics to describe the quantum world. In financial markets, there are limits as to what we can know at any one point in time regardless how much data we analyze. It's the nature of the beast.
The Trinity Of Errors In Financial Models: An Introductory Analysis Using TensorFlow Probability
"
Finance is not a precise predictive science like physics. Not even close. So let’s not treat academic theories and models of finance as if they were models of quantum physics.
All financial models, whether based on academic theories or data mining strategies, are at the mercy of the trinity of modeling errors. While this trifecta of errors can be mitigated with appropriate modeling tools, it cannot be eliminated. There will always be asymmetry of information and cognitive biases. Models of asset values and risks will change over time due to the dynamic nature of capitalism, human behavior, and technological innovation."