A finite horizon optimal multiple switching problem

Boualem Djehiche, Said Hamadène, Alexandre Popier

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of optimal multiple switching in a finite horizon when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and solved using probabilistic tools such as the Snell envelope of processes and reflected backward stochastic differential equations. Finally, when the state of the system is a Markov process, we show that the associated vector of value functions provides a viscosity solution to a system of variational inequalities with interconnected obstacles.

Original languageEnglish (US)
Pages (from-to)2751-2770
Number of pages20
JournalSIAM Journal on Control and Optimization
Volume48
Issue number4
DOIs
StatePublished - 2009

Keywords

  • Backward stochastic differential equations
  • Impulse control
  • Optimal switching
  • Real options
  • Snell envelope
  • Stopping time
  • Variational inequalities

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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