A. İ. Çekiç, R. Korn, Ö. Uğur, A Mean-Square Approach to Constant Proportion Debt Obligations, Wilmott Magazine, Issue **53**, Technical Paper, (May 2011).

Re-printed in 2016.

### Abstract

In this paper we show that the optimal leverage function for CPDOs in a mean-square sense coincides with the one used in practise. However, the optimal strategy will lead to a sure shortfall, i.e. losses are unavoidable. We solve the corresponding problem using two different approaches, the optimal control approach and the martingale method leading to explicit formulae for the leverage strategy, the wealth process, and the final shortfall.

*Keywords*: constant proportional debt obligation, stochastic control, Hamilton-Jacobi-Bellmann equation, martingale method