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Optimal stopping of expected profit and cost yields in an investment under uncertainty

Author

Listed:
  • Boualem Djehiche

    (KTH Stockolm)

  • Said Hamad`ene

    (LMM)

  • Marie Am'elie Morlais

    (LMM)

Abstract

We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell envelopes for the profit and cost yields which act as obstacles to each other. We then construct both a minimal and a maximal solutions using an approximation scheme of the associated system of reflected backward SDEs. When the dependence of the cash-flows on the sources of uncertainty, such as fluctuation market prices, assumed to evolve according to a diffusion process, is made explicit, we also obtain a connection between these solutions and viscosity solutions of a system of variational inequalities (VI) with interconnected obstacles. We also provide two counter-examples showing that uniqueness of solutions of (VI) does not hold in general.

Suggested Citation

  • Boualem Djehiche & Said Hamad`ene & Marie Am'elie Morlais, 2010. "Optimal stopping of expected profit and cost yields in an investment under uncertainty," Papers 1001.3289, arXiv.org.
    • Handle: RePEc:arx:papers:1001.3289
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    References listed on IDEAS

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    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    2. Ralf Korn, 1999. "Some applications of impulse control in mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 493-518, December.
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