Optimal Securitization of Credit Portfolios via Impulse Control

Rüdiger Frey and Roland C. Seydel

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Submission date: 07. Sep. 2009 (revised version: October 2009)
Pages: 35
published in: Mathematics and financial economics, 4 (2010) 1, p. 1-28 
DOI number (of the published article): 10.1007/s11579-010-0033-y
Bibtex
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.