Optimising Credit Portfolio Using a Quadratic Nonlinear Projection Method

TL;DR

This paper introduces a quadratic nonlinear projection method for optimizing credit portfolios with CVaR risk measurement, enabling efficient handling of nonlinear objectives like return-to-risk ratio and diversification index.

Contribution

The paper presents a novel quadratic nonlinear projection framework for credit portfolio optimization that accommodates general nonlinear objectives and uses a series of locally approximated single-step optimizations.

Findings

Effective optimization of credit portfolios with CVaR risk measure.

Flexible handling of nonlinear objectives such as return-to-risk ratio.

Method provides locally exact solutions using Lagrange multipliers.

Abstract

A novel optimisation framework through quadratic nonlinear projection is introduced for credit portfolio when the portfolio risk is measured by Conditional Value-at-Risk (CVaR). The whole optimisation procedure to search toward the optimal portfolio state is conducted by a series of single-step optimisations under the local constraints described in the multi-dimensional constraint parameter space as functions of the total amount of portfolio adjustment. Each single-step optimisation is approximated by the first-order variation of the weight increments with respect to the total amount of portfolio adjustment and is solved in the form of locally exact formula formulated in the general Lagrange multiplier method. Our method can deal with optimisation for general nonlinear objective functions, such as the return-to-risk ratio maximisation or the diversification index, as well as the risk minimisation or the return maximisation.