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Wolfgang Breytmann, Julio Deride, Nicolás Hernández · 2026-07-06
The paper studies how solutions to a discrete-time option/contingent-claim pricing problem behave when you slightly perturb the assumed probability distribution, the payoff, or both. Using a mathematical framework (Rockafellian perturbations and epi/hypo-convergence), it shows conditions under which the pricing and its dual 'shadow prices' converge stably, links the duality gap to the value of perfect information, and gives examples where stability breaks down due to rare-but-extreme scenarios.
Why it matters: For those pricing or hedging derivatives under uncertain probability models, the work characterizes when small modeling errors lead to small pricing errors versus when they cause instability. It flags that low-probability, high-impact scenarios can make claim valuations ill-conditioned, which is a useful cautionary point for risk and model-robustness work.
⚠ This is an abstract mathematical stability result with no empirical testing or trading application — it is theory about well-posedness, not a usable pricing or trading method.
We study the stability of solutions to the discrete-time contingent-claim problem over a finite investment horizon when uncertainty is modeled by random variables with finite discrete support. Our main contribution is to use Rockafellian perturbations as a framework for this stability analysis: we construct perturbations of the underlying probability distribution, of the contingent claim, and of both jointly, and we establish epi-convergence of the corresponding approximating Rockafellians for the primal problem. The associated hypo-convergent approximations yield stable dual problems which, in turn, imply convergence of the dual variables, interpreted as shadow prices. This analysis reveals a connection between the duality gap and the value of perfect information and it provides conditions under which strong duality holds. We also construct examples in which epi-convergence fails due to critical scenarios with vanishing probabilities but unbounded impacts, illustrating the boundary between well-behaved and ill-conditioned contingent-claim problems.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.