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Convex integral functionals of càdlàg processes

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  • Perkkiö, Ari-Pekka
  • Treviño-Aguilar, Erick

Abstract

This article characterizes conjugates and subdifferentials of convex integral functionals over linear spaces of càdlàg stochastic processes. The approach is based on new measurability results on the Skorokhod space and new interchange rules of integral functionals that are developed in the article. The main results provide a general approach to apply convex duality in a variety of optimization problems ranging from optimal stopping to singular stochastic control and mathematical finance.

Suggested Citation

  • Perkkiö, Ari-Pekka & Treviño-Aguilar, Erick, 2025. "Convex integral functionals of càdlàg processes," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002692
    DOI: 10.1016/j.spa.2024.104561
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    References listed on IDEAS

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    1. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Post-Print hal-02373296, HAL.
    2. Boetius, Frederik & Kohlmann, Michael, 1998. "Connections between optimal stopping and singular stochastic control," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 253-281, September.
    3. Pennanen, Teemu & Perkkiö, Ari-Pekka, 2018. "Convex integral functionals of regular processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1652-1677.
    4. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    5. Czichowsky, Christoph Johannes & Peyre, Rémi & Schachermayer, Walter & Yang, Junjian, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," LSE Research Online Documents on Economics 85230, London School of Economics and Political Science, LSE Library.
    6. Pennanen, Teemu & Perkkiö, Ari-Pekka, 2023. "Dual spaces of cadlag processes," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 69-93.
    7. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Finance and Stochastics, Springer, vol. 22(1), pages 161-180, 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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