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I am doing a dissertation in finance on a maths degree. I wanted to forecast stock prices using artifcial neural networks but none of my tutors are able to supervise so I'm having to do something else.

I would like to do something similar, something that I could also use for my own personal use. If possible, please suggest some mathematical models.

Anything cool that I could do with a differential equation? I am open to other topics too, but something with which I could actually make some money. Or atleast aid my investment decision making with.

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The reasons why your Professors were unaware of neural networks in forecasting stock prices is because, if you intend to model stock prices alone, it does not work, hence nothing has surpassed either ARIMA modelling or adaptive filtering, eg. Kalman filters. The reason why NN does not work is because they can be easily trained to perfectly fit the training data, but they have virtually no forward predictability on test data, as they by the nature of the method overfit a model. However, NN can be very accurate in forecasting prices using factor methods, eg. linking ice cream stocks to such things as daily temperature, season, GDP, Disposable income, etc. But not on prices alone. It is hard to see how you have got to do a Ph.D. when fundamentally do not understand that a differential equation gives either an unstable or stable solution( I am making an assumption here, I could be incorrect, you may be aware), given that the BS formula can be derived by a differential equation analogous to Einstein's heat diffusion equation, it is possible a prediction within a range is possible, it is in the realm of econophysics, which I will leave for others.

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  • $\begingroup$ A perhaps more valuable PhD would be to look at Wiener processes eg, Brownian motion with drift, drift and variance are the two moments captured by the model, look at means over time, their stability and predictability may be more helpful, trying to predict stock prices is impossible, read Benoit Mandelbrot's The Misbehaviour of Markets. Most forecasts rely on probability and fall within a range, no single point price prediction can be accurate often enough to be usefull. $\endgroup$
    – Con Fluentsy
    Dec 15, 2020 at 20:52
  • $\begingroup$ It is for a bachelors thesis, not PhD. I was thinking Geometric Brownian Motion. I read some papers and people seem to be getting pretty accurate forecasts. With ANN they also get accurate forecasts, at least in the papers, I'm not sure how it works in reality but I'm assuming they are good since it works for some? I don't undestand why you are so sceptical $\endgroup$
    – PlatinumMaths
    Dec 17, 2020 at 18:46
  • $\begingroup$ Because I have 30 years experience in data mining, and time series modelling,I remember back in 1985, one of the investment banks touted there new revolutionary price prediction models based on neural networks,this faded into oblivion like they all do, there is not enough space to fully explain why it does not work,backfitting is dead easy to be spot on,are you sure they were blind forward projections, there is some revolutionary work with nn and arima,by Rob Hyndman. Monash University professor and creator of forecast package in R ,try his stuff,fully explained,for students. $\endgroup$
    – Con Fluentsy
    Dec 20, 2020 at 1:18
  • $\begingroup$ By nn,i mean ann,convoluted nn,and all variants. $\endgroup$
    – Con Fluentsy
    Dec 20, 2020 at 1:19

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