Optimal Securitization of Credit Portfolios via Impulse Control

revised version: October 2009
Rüdiger Frey, and Roland C. Seydel
(Please use for correspondence this email).

Submission date: 07. Sep. 2009
Pages: 35
MSC-Numbers: 35B37, 49L25, 49N25, 91B28, 91B70, 93E20
Keywords and phrases: Securitization, credit portfolios, impulse control, Markov-switching economy, combined stochastic control, viscosity solutions, quasi-variational inequalities, iterated optimal stopping
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Abstract:
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.