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I'm aware that there is an entire field of mathematical finance, but I have not looked into it. I know quantitative finance also works as a team and is not practically doable as an individual. However, as I want to make more logical decisions, instead of based on my instinct, I wonder if I can actively apply my knowledge but without too much time involvement.

My research is in continuous optimization, specifically convex optimization, polynomial optimization, and semidefinite programming. I know how to code and some basic math such as in topology, functional analysis, stochastic processes, etc. I'm still learning more math in different areas every year, but I'm far from the research level.

So while not going very deep, I wonder if there is anything I can do with this basic knowledge in optimization and mathematics. I know my university offers an optimization in finance class but I did not take that.

So as an individual, with limited time and not much knowledge in finance, how can I approach my own investment such that it can be conducted more quantitatively and reasonably?

I might be more interested in the long term due to my limited time. But if I don't need to spend much time every week, short term is also fine.

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    If you ask in the quant stack, you will probably get several conflicting pieces of advice on how to apply advanced mathematicians to the market. My own reaction is that if it worked, the pros would be a lot more successful than they are.
    – keshlam
    Commented Apr 19 at 2:46
  • @keshlam Thank you. I'll ask on the quant stack as well then. I would want to trust something else other than my instincts. Of course, if I can duplicate my brain 10 times it would be great, but as I have limited time, I would also love to hear basic ideas if any. Commented Apr 19 at 2:50
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    Obligatory XKCD. Jokes aside, start by investing through a broad-market index fund and continue to educate yourself (see mhoran_psprep's answer below). "Premature optimization is the root of all evil" applies to personal finance, too.
    – 0xFEE1DEAD
    Commented Apr 20 at 2:40

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An approach that will use your math and computer skills:

  • Keep studying
  • Put the money you want to invest into index funds that cover a broad swath of the market.
  • Get a well paying job, and start investing for retirement.
  • Study the performance of active mutual funds, ETFs, and individual investors and realize that even the quants don't win all the time.

So while not going very deep, I wonder if there is anything I can do with this basic knowledge in optimization and mathematics. I know my university offers an optimization in finance class but I did not take that.

So as an individual, with limited time and not much knowledge in finance, how can I approach my own investment such that it can be conducted more quantitatively and reasonably?

In the world of investing there are many areas to study optimization. You could determine a more optimal schedule for rebalancing. You could determine a better method to determine when a person considering retirement should start to receive social security or a pension.

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