Approximation of Optimal Stopping Problems and Variational Inequalities Involving Multiple Scales in Economics and Finance

  • Andrianos E. Tsekrekos
  • Athanasios N. Yannacopoulos


Many interesting decision-making problems in economics and finance can be expressed in terms of variational inequalities, whose well-developed theory provides valuable answers and insights concerning optimal policies. In this chapter, we first provide a brief introduction to the theory of variational inequalities as applied to economic decision-making, before focusing on a particular class (optimal stopping problems) where the underlying Markov process that introduces the uncertainty in the setting presents evolution of multiple time scales. Such problems lead to variational inequalities with fast-varying coefficients which require techniques related to homogenisation theory. Our results establish how, for such problems, approximate solutions to any order and (importantly) in almost closed form can be obtained by a singular perturbation approach. Our example from the waiting-to-invest literature in the last section demonstrates the applicability of the results.


Economic decision-making Variational inequalities Optimal stopping problems Multi-scale volatility 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Andrianos E. Tsekrekos
    • 1
  • Athanasios N. Yannacopoulos
    • 2
  1. 1.Department of Accounting and FinanceSchool of Business, Athens University of Economics and BusinessAthensGreece
  2. 2.Department of Statistics, School of Information Sciences and TechnologyAthens University of Economics and BusinessAthensGreece

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