We analyze the martingale selection problem of Rokhlin in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in models spanning frictionless markets, models with proportional transaction costs, and models for illiquid markets. In all these models, we also incorporate trading constraints.
Robust martingale selection problem and its connections to the no-arbitrage theory / M. Burzoni, M. Sikic. - In: MATHEMATICAL FINANCE. - ISSN 0960-1627. - 30:1(2020 Jan), pp. 260-286. [10.1111/mafi.12225]
Robust martingale selection problem and its connections to the no-arbitrage theory
M. Burzoni;
2020
Abstract
We analyze the martingale selection problem of Rokhlin in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in models spanning frictionless markets, models with proportional transaction costs, and models for illiquid markets. In all these models, we also incorporate trading constraints.
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