[1] Madan is most known for his work on the variance gamma model, the fast Fourier transform method for option pricing, and the development of Conic Finance.

[5] He has authored numerous publications spanning the areas of financial markets, general equilibrium theory, and mathematical finance including books and articles in peer-reviewed journals.

[8] Focusing his research efforts on credit value adjustments, his study proposed a theory of capital requirements to address the problem of cross-default exposures.

[10] He also introduced a conic finance-based nonlinear equity valuation model, which integrated risk charges contingent upon measure distortions.

[12][13] While exploring the valuation of European call options employing the Vasicek-Gaussian stochastic process, his research proposed an approach to approximate and determine the equilibrium change of measure in incomplete markets, using log return mean, variance, and kurtosis.

[14] In a collaborative study with Robert A. Jarrow, he demonstrated the application of term-structure-associated financial instruments in formulating dynamic portfolio management tactics, specifically aimed at mitigating distinct systematic jump hazards inherent in asset returns.

[19] His recent work in 2021 has contributed to the understanding of risk-neutral densities and jump arrival tails by introducing theoretical examples and practical models based on quasi-infinitely divisible distributions.