Finding Research Problems in Financial Mathematics
Summary
The document considers how a mathematically trained researcher can find publishable questions in financial mathematics, especially beyond algorithmic trading. Its answer cautions that identifying problems with academic value and broader economic or social relevance can be difficult. It points toward foundational questions in stock and bond markets as well as derivatives, which dominate many mathematical finance books.
One example is modeling financial markets as networks of money and securities flows. Studying how the network’s structure affects market efficiency and elasticity could offer insights relevant to researchers and regulators. The discussion is suggestive rather than a research roadmap: it poses an area of inquiry without giving a solved problem, methods, or empirical evidence. It also notes that this network perspective may not suit researchers focused on stochastic calculus, underscoring that suitable topics depend on a person’s mathematical interests.
Key ideas
- Publishable financial mathematics problems can be hard to identify when academic and broader social relevance are both goals.
- Research questions can concern stock and bond markets as well as derivatives.
- A network representation of money and securities flows offers a possible direction for studying market structure.
- The effect of flow topology on market efficiency and elasticity may be relevant to regulators.
- The proposed direction is exploratory and may not fit researchers whose expertise centers on stochastic calculus.
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Full text
# How to find interesting open math problems in quantitative finance that I could publish articles about? # How to find interesting open math problems in quantitative finance that I could publish articles about? Which books on financial mathematics would you recommend for people with good background in probability, statistics and stochastic processes but without any background in financial mathematics? The goal is the next one: to find interesting mathematical problems in financial mathematics, solve it (using methods of probability, statistics and stochastic processes) and publish an article about it. So the question is related to scientific work, not with industry. And the question is not about algorithms or something like that. If my question is too general then which books on main branches of financial mathematics would you recommend? The only books I've heard of is books of https://en.wikipedia.org/wiki/Mark_S._Joshi. ## Answer by Michael Isichenko (score 2) https://quant.stackexchange.com/a/75999 I think it is difficult to come up with an open problem in math finance that is also economically/socially relevant. And I don't mean to say "practitioner" relevant, as you mentioned you are looking for a topic for your academic research. Granted, derivatives are more mathematical than underlyings, and are disproportionately represented math fin books. But I think there are also good fundamental questions in stock and bond markets that require a better math than money-making trading algos. I recently discussed, and more posed than solved, one of such problems related to flow networks describing cyclic and acyclic flow of money and securities in a broad financial market: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4473754. If you are an Ito formula person, this is probably not your thing. But any contribution to understanding how the topology of money flows affect efficiency and elasticity of the markets would probably be of broad interest, including for regulatory consideration.
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