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October  2016, 12(4): 1323-1331. doi: 10.3934/jimo.2016.12.1323

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

 1 Paris School of Economics, University of Paris 1, Panthéon Sorbonne, France 2 Paris School of Economics, University of Paris 1, Panthéon Sorbonne, CNRS, CES. M.S.E. 106 Boulevard de l'Hôpital, 75647 Paris cedex 13, France 3 King Saud University, College of Science, Department of Mathematics, Box 2455, Riyadh 11451, Saudi Arabia 4 Department of Mathematics, Swiss Federal Institute of Technology (ETH) Zurich and Swiss Finance Institute, Switzerland

Received  February 2015 Revised  October 2015 Published  January 2016

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.
Citation: Senda Ounaies, Jean-Marc Bonnisseau, Souhail Chebbi, Halil Mete Soner. Merton problem in an infinite horizon and a discrete time with frictions. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1323-1331. doi: 10.3934/jimo.2016.12.1323
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