Research Topics in Financial Mathematics: Incomplete Markets and Rates

Summary

The document asks which problems remain important in stochastic financial mathematics, beyond proposing asset-price processes and studying log-return distributions. The response offers two personal research interests: pricing and hedging in incomplete markets, especially for credit derivatives, and modeling discounting and tenor basis in interest-rate markets. These topics point toward practical challenges where market structure and imperfect hedging matter alongside mathematical modeling.

The evidence is a short list of suggested areas and references on multiple interest-rate curves. It does not explain particular methods, compare approaches, or report empirical results. The recommendations are presented as one respondent’s preferences, not as a comprehensive survey or ranked account of current research. Readers seeking research directions will need to consult the cited literature and assess how the questions have evolved since it was written.

Key ideas

• Incomplete-market pricing and hedging remain potential research areas, particularly for credit derivatives.
• Interest-rate research can examine stochastic discounting and differences between tenor curves.
• The response presents personal suggestions rather than a comprehensive review of the field.

Tags

# Modern problems in financial mathematics


# Modern problems in financial mathematics












I have a MSc degree in the area of Financial Mathematics, but I am doing research now in other field of stochastics. Could you please tell me about the most important problems of (stochastic) financial mathematics nowadays?

Are they only looking for new processes for they price of an asset (and solutions of corresponding pricing problems)? Maybe they also wondering about distributions of log-returns? - these are the problem which seems to be always actual and I remember it.

If there are any other striking problems? Please do not hesitate to make just suppositions - what are the important problems in your opinion.

## Answer by quant_dev (score 7, accepted)

https://quant.stackexchange.com/a/907

My personal favourites:

- pricing and hedging in incomplete markets, in particular credit derivatives

- stochastic prediction-discount and inter-tenor basis in the interest rate market; see "Two curves, one price" (Bianchetti) and "Interest Rates and The Credit Crunch: New Formulas and Market Models " (Mercurio)

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