Merton problem in an infinite horizon and a discrete time with frictions

Senda Ounaies, Jean Marc Bonnisseau, Souhail Chebbi, Halil Mete Soner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We investigate the problem of optimal investment and consumption of Merton in the case of discrete markets in an infinite horizon. We suppose that there is frictions in the markets due to loss in trading. These frictions are modeled through nonlinear penalty functions and the classical transaction cost and liquidity models are included in this formulation. In this context, the solvency region is defined taking into account this penalty function and every investigator have to maximize his utility, that is derived from consumption, in this region. We give the dynamic programming of the model and we prove the existence and uniqueness of the value function.

Original languageEnglish (US)
Pages (from-to)1323-1331
Number of pages9
JournalJournal of Industrial and Management Optimization
Issue number4
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics


  • After liquidation value
  • Discrete market
  • Dynamic programming
  • Infinite horizon
  • Market frictions
  • Merton problem
  • Value function


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