Optimal securitization of credit portfolios via impulse control

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.

On the Modelling of Impulse Control with Random Effects for Continuous Markov Processes

“…An alternate approach for modelling the impulse-controlled process (see e.g., Menaldi (1980), Alvarez (2004), Øksendal and Sulem (2005), Jack and Zervos (2006), Frey and Seydel (2010), Helmes et al (2015)) is to start with a given filtered probability space (Ω, F , {F t }, P) on which the fundamental evolution of the process can be defined for each initial distribution. The impulse-controlled process is then constructed iteratively over the successive intervals {[τ k , τ k+1 )} by pasting together a shift of the fundamental process having the required different initial positions given by the impulses.…”