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Optimal Securitization of Credit Portfolios via Impulse Control
Rüdiger Frey and Roland C. SeydelAbstract
We study the optimal loan securitization policy of a commercial bank which is mainly engaged in lending activities. For this we propose a stylized dynamic model which contains the main features affecting the securitization decision. In line with reality we assume that there are non-negligible fixed and variable transaction costs associated with each securitization. The fixed transaction costs lead to a formulation of the optimization problem in an impulse control framework. We prove viscosity solution existence and uniqueness for the quasi-variational inequality associated with this impulse control problem. Iterated optimal stopping is used to find a numerical solution of this PDE, and numerical examples are discussed.
- Received:
- 07.09.09
- Published:
- 11.09.09
- MSC Codes:
- 35B37, 49L25, 49N25, 91B28, 91B70, 93E20
- Keywords:
- Securitization, credit portfolios, impulse control, Markov-switching economy, combined stochastic control, viscosity solutions, quasi-variational inequalities, iterated optimal stopping