The explicit solution to a sequential switching problem with non-smooth data

Timothy C. Johnson, Mihail Zervos

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We consider the problem faced by a decision maker who can switch between two random payoff flows. Each of these payoff flows is an additive functional of a general 1D Itô diffusion. There are no bounds on the number or on the frequency of the times at which the decision maker can switch, but each switching incurs a cost, which may depend on the underlying diffusion. The objective of the decision maker is to select a sequence of switching times that maximizes the associated expected discounted payoff flow. In this context, we develop and study a model in the presence of assumptions that involve minimal smoothness requirements from the running payoff and switching cost functions, but which guarantee that the optimal strategies have relatively simple forms. In particular, we derive a complete and explicit characterization of the decision maker's optimal tactics, which can take qualitatively different forms, depending on the problem data. © 2010 Taylor & Francis.

Original languageEnglish
Pages (from-to)69-109
Number of pages41
JournalStochastics: An International Journal of Probability and Stochastic Processes
Volume82
Issue number1
DOIs
Publication statusPublished - Feb 2010

Keywords

  • Optimal switching
  • Sequential entry and exit decisions
  • Stochastic impulse control
  • System of variational inequalities

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