Are PDEs helpful for stocks

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11/8/08
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Hello,

I would like to check what do you think about the application of PDEs to stock(stocks, not options or any derivatives). I am quite new to the field of mathematical finance.I have a graduate degree in philosophy and I've done work on mathematical logic, set theory, formal languages... etc. I am now taking classes in calculus and linear algebra and reading a book on arbitrage. I know traders use a set of technical indicators. However I found some attractive combinations in modeling which can be suitable for stocks. Probably stocks are less bounded than bonds or options but that opens bigger gap for more extensive research(binomial trees, stochastic calculus, pde) and risk minimization. I tend to think that if stocks' random space is relatively modeled it could translate to more paths leading to stability than the paths we can find with options.
 
Hi Barchowski,

PDEs are very costly in high-dimensional spaces.
So I recommend to estimate PDEs for a single stock, but dissuade using PDEs in high-dimensional problems like portfolio optimization.

If you are interested in such issue, I'll advise you to read this book: Large-Scale PDE-Constrained Optimization!

regards
Bastian
 
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