What Black-Scholes Research Problem Could I Explore for a 20-30 Page Math Paper?

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SUMMARY

The discussion centers on identifying research problems related to the Black-Scholes model for a 20-30 page mathematics paper. Participants suggest three distinct approaches: developing original mathematics through new theorems and proofs, applying known mathematics to unique problems that extend beyond elementary textbook examples, and exploring specialized aspects of the Black-Scholes model that provide deeper insights than standard textbooks. Clear definitions of what constitutes a "research paper" are emphasized to guide the problem construction process.

PREREQUISITES
  • Understanding of Black-Scholes equations and their applications in finance.
  • Familiarity with mathematical proof techniques and theorem development.
  • Knowledge of advanced calculus and differential equations.
  • Ability to conduct literature reviews on mathematical finance topics.
NEXT STEPS
  • Research original mathematical contributions to the Black-Scholes model.
  • Explore case studies applying Black-Scholes to non-standard financial instruments.
  • Investigate specialized literature on the limitations and extensions of the Black-Scholes model.
  • Learn about mathematical proof strategies relevant to finance-related research.
USEFUL FOR

Mathematics students, financial analysts, and researchers interested in exploring advanced topics in mathematical finance, particularly those focusing on the Black-Scholes model.

MrMumbleX
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I don't exactly understand Black-Scholes equations, but I need a problem involving Black-Scholes for a 20-30 page math research paper. Would someone please give me a good problem or some suggestions on how to construct the problem?
 
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You need to define "research paper" precisely. It could mean:

1. Original mathematics - new theorems, proofs etc.
2. Routine application of known mathematics to a problem that has a few particular details that keep it from being an elementary textbook problem
3. A paper that explains specialized aspects of a topic - known mathematics but more than is in your textbook. This might be called a "term paper".
 

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