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

Senda Ounaies (1) , Jean-Marc Bonnisseau (1, 2) , Souhail Chebbi (3) , Mete H. Soner (4)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics
3 KSU - King Saud University [Riyadh]
4 D-MATH - Department of Mathematics [ETH Zurich]

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.

Mots clés: Merton problem; discrete market; infinite horizon; market frictions; after liquidation value; dynamic programming; value function.

Domaines: Economies et finances

Senda Ounaies, Jean-Marc Bonnisseau, Souhail Chebbi, Mete H. Soner. Merton problem in an infinite horizon and a discrete time with frictions. Journal of Industrial and Management Optimization, 2016, 12 (4), pp.1323-1331. ⟨10.3934/jimo.2016.12.1323⟩. ⟨halshs-01395604⟩