Portfolio optimization under credit risk (Q1424641)

A financial market model is considered which describes the dynamics of the non-defaultable short rate (\(r\)), the defaultable short rate (\(s\)) and the uncertainty index (\(u\)). Stochastic differential equations by a standard Brownian motion are used to describe \((r(t),s(t),u(t))\). The prices of non-defaultable and defaultable discount bonds are evaluated. The problem of portfolio optimization in this model is reduced to a linear mixed-integer programming problem. An application to the portfolio of German, Italy and Greece sovereign bonds is discussed.