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Stopper-Controller Games embedded in Single-Player Control Problems

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Listed:
  • Martin Larsson
  • Marvin S. Mueller
  • Josef Teichmann

Abstract

In 2002, Benjamin Jourdain and Claude Martini discovered that for a class of payoff functions, the pricing problem for American options can be reduced to pricing of European options for an appropriately associated payoff, all within a Black-Scholes framework. This discovery has been investigated in great detail by S\"oren Christensen, Jan Kallsen and Matthias Lenga in a recent work in 2020. In the present work we prove that this phenomenon can be observed in a wider context, and even holds true in a setup of non-linear stochastic processes. We analyse this problem from both probabilistic and analytic viewpoints. In the classical situation, Jourdain and Martini used this method to approximate prices of American put options. The broader applicability now potentially covers non-linear frameworks such as model uncertainty and controller-and-stopper-games.

Suggested Citation

  • Martin Larsson & Marvin S. Mueller & Josef Teichmann, 2020. "Stopper-Controller Games embedded in Single-Player Control Problems," Papers 2006.09493, arXiv.org.
    • Handle: RePEc:arx:papers:2006.09493
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    References listed on IDEAS

    as
    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    2. Soren Christensen & Jan Kallsen & Matthias Lenga, 2020. "Are American options European after all?," Papers 2002.05571, arXiv.org.
    3. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    4. Nutz, Marcel & van Handel, Ramon, 2013. "Constructing sublinear expectations on path space," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3100-3121.
    5. Denk, Robert & Kupper, Michael & Nendel, Max, 2019. "A Semigroup Approach to Nonlinear Lévy Processes," Center for Mathematical Economics Working Papers 610, Center for Mathematical Economics, Bielefeld University.
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