Geodesic
An equilibrium model of debt and bankruptcy
Bressan, Alberto1  ; Nguyen, Khai T.1
1 Department of Mathematics, Penn State University, University Park, PA 16802, USA.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 953-982

Voir la notice de l'article provenant de la source Numdam

We study optimal strategies for a borrower, who services a debt in an infinite time horizon, taking into account the risk of possible bankruptcy. In a first model, the interest rate as well as the instantaneous bankruptcy risk are given, increasing functions of the total amount of debt. In a second model only the bankruptcy risk is given, while the interest rate is determined from a Nash equilibrium, in a game between the borrower and a pool of risk-neutral lenders. This yields a non-standard optimal control problem for the borrower, where the dynamics involves all future values of the control. For this model, optimal repayment strategies are constructed, in open-loop form. In addition, for optimal strategies in feedback form, our analysis shows that the value function should satisfy a new kind of nonlinear, degenerate elliptic equation.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016030
Classification : 49J15, 49N90
Keywords: Optimal control, differential game, optimal debt management, bankruptcy risk

Bressan, Alberto 1 ; Nguyen, Khai T. 1

1 Department of Mathematics, Penn State University, University Park, PA 16802, USA. 
@article{COCV_2016__22_4_953_0,
     author = {Bressan, Alberto and Nguyen, Khai T.},
     title = {An equilibrium model of debt and bankruptcy},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {953--982},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {4},
     year = {2016},
     doi = {10.1051/cocv/2016030},
     zbl = {1353.49050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016030/}
}
TY  - JOUR
AU  - Bressan, Alberto
AU  - Nguyen, Khai T.
TI  - An equilibrium model of debt and bankruptcy
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2016
SP  - 953
EP  - 982
VL  - 22
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016030/
DO  - 10.1051/cocv/2016030
LA  - en
ID  - COCV_2016__22_4_953_0
ER  - 
%0 Journal Article
%A Bressan, Alberto
%A Nguyen, Khai T.
%T An equilibrium model of debt and bankruptcy
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2016
%P 953-982
%V 22
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016030/
%R 10.1051/cocv/2016030
%G en
%F COCV_2016__22_4_953_0
Bressan, Alberto; Nguyen, Khai T. An equilibrium model of debt and bankruptcy. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 953-982. doi: 10.1051/cocv/2016030

Cité par Sources :