  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.
