Robust Optimization of Credit Portfolios

TL;DR

This paper develops a robust optimization framework for credit portfolios that accounts for model misspecification, providing explicit strategies and solutions via recursive HJB equations for risk-averse investors.

Contribution

It introduces a novel dynamic credit portfolio model that explicitly incorporates robustness against model misspecification using a max-min optimization approach.

Findings

Explicit characterization of robust bond investment strategies

Solutions obtained through recursive HJB equations

Truncation method ensures unique bounded solutions

Abstract

We introduce a dynamic credit portfolio framework where optimal investment strategies are robust against misspecifications of the reference credit model. The risk-averse investor models his fear of credit risk misspecification by considering a set of plausible alternatives whose expected log likelihood ratios are penalized. We provide an explicit characterization of the optimal robust bond investment strategy, in terms of default state dependent value functions associated with the max-min robust optimization criterion. The value functions can be obtained as the solutions of a recursive system of HJB equations. We show that each HJB equation is equivalent to a suitably truncated equation admitting a unique bounded regular solution. The truncation technique relies on estimates for the solution of the master HJB equation that we establish.