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Stability and Dual Valuation of Contingent Claims under Rockafellian Perturbations

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  • Wolfgang Breytmann
  • Julio Deride
  • Nicol'as Hern'andez

Abstract

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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  • Wolfgang Breytmann & Julio Deride & Nicol'as Hern'andez, 2026. "Stability and Dual Valuation of Contingent Claims under Rockafellian Perturbations," Papers 2607.05697, arXiv.org.
    • Handle: RePEc:arx:papers:2607.05697
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    1. PInar, Mustafa Ç. & Salih, AslIhan & CamcI, Ahmet, 2010. "Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming," European Journal of Operational Research, Elsevier, vol. 201(3), pages 770-785, March.
    2. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
    3. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Alessandro Beber & Daniela Fabbri & Marco Pagano & Saverio Simonelli, 2021. "Short-Selling Bans and Bank Stability," The Review of Corporate Finance Studies, Society for Financial Studies, vol. 10(1), pages 158-187.
    5. Yuhong Xu, 2014. "Robust valuation and risk measurement under model uncertainty," Papers 1407.8024, arXiv.org.
    6. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    7. Paul Glasserman & Xingbo Xu, 2014. "Robust risk measurement and model risk," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 29-58, January.
    8. Teemu Pennanen & Ari-Pekka Perkkiö, 2018. "Convex duality in optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 22(4), pages 733-771, October.
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