What question did this study set out to answer?

To determine whether a weakly continuous family of probability measures on R² increasing in convex order can be realized as a càdlàg Markov martingale relative to its completed, right-continuous natural filtration.

August 19, 2026Open Access

On the Planar Kellerer Problem for Two-Asset Markov–Martingale Calibration

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Authors

SSShantanu SrivastavaMotilal Nehru National Institute of Technology

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Implication

Mathematical analysis demonstrates obstructions to right-continuous Markov-martingale realizations in two dimensions, highlighting geometric limits in multi-asset calibration.

Key Points

To determine whether a weakly continuous family of probability measures on R² increasing in convex order can be realized as a càdlàg Markov martingale relative to its completed, right-continuous natural filtration.
Designed an elementary four-atomic planar construction with alternating coordinate variations across dyadic time steps accumulating near zero.
Analyzed the preservation of an axis label enforced by matching coordinate second moments within the right-continuous germ sigma-field at time zero.
Demonstrated that the deterministic initial state fails to encode the preserved axis label, creating an explicit obstruction to the Markov property under completed right-continuous filtrations.
Established that this obstruction is specific to right-continuization and does not rule out Markovian realizations under the raw natural filtration.

Cite This Study

Shantanu Srivastava (2026) studied this question.

synapsesocial.com/papers/6a85633c03308d306e2d64b9 https://doi.org/10.5281/zenodo.21969883

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Implication

Mathematical analysis demonstrates obstructions to right-continuous Markov-martingale realizations in two dimensions, highlighting geometric limits in multi-asset calibration.

On the Planar Kellerer Problem for Two-Asset Markov–Martingale Calibration

Discussion

Member takes

Implication

Key Points

Cite This Study

On the Planar Kellerer Problem for Two-Asset Markov–Martingale Calibration

Discussion

Member takes

Implication

Key Points

Cite This Study

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