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.
Accepté le :
DOI : 10.1051/cocv/2016030
Mots clés : Optimal control, differential game, optimal debt management, bankruptcy risk
@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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. http://www.numdam.org/articles/10.1051/cocv/2016030/
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