Reducing the debt : is it optimal to outsource an investment?

Gilles Edouard Espinosa (1) , Caroline Hillairet (2) , Benjamin Jourdain (1, 3) , Monique Pontier (4)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 MATHRISK - Mathematical Risk Handling
4 IMT - Institut de Mathématiques de Toulouse UMR5219

We deal with the problem of outsourcing the debt for a big investment, according two situations: either the firm outsources both the investment (and the associated debt) and the exploitation to a private consortium, or the firm supports the debt and the investment but outsources the exploitation. We prove the existence of Stackelberg and Nash equilibria between the firm and the private consortium, in both situations. We compare the benefits of these contracts. We conclude with a study of what happens in case of incomplete information, in the sense that the risk aversion coefficient of each partner may be unknown by the other partner.

Keywords: Optimization; Nash equilibrium; Stackelberg equilibrium; Partial information; Stochastic control; Outsourcing; Public Debt; Public-Private-Partnership

Domains: Probability [math.PR]; Computational Finance [q-fin.CP]

Gilles Edouard Espinosa, Caroline Hillairet, Benjamin Jourdain, Monique Pontier. Reducing the debt : is it optimal to outsource an investment?. Mathematics and Financial Economics, 2016, 10 (4), pp.457-493. ⟨10.1007/s11579-016-0166-8⟩. ⟨hal-00824390v2⟩