  We study the problem of determining risk-minimizing investment strategies for
insurance payment processes in the presence of taxes and expenses. We consider
the situation where taxes and expenses are paid continuously and symmetrically
and introduce the concept of tax- and expense-modified risk-minimization.
Risk-minimizing strategies in the presence of taxes and expenses are derived
and linked to Galtchouk-Kunita-Watanabe decompositions associated with modified
versions of the original payment processes. Furthermore, we show equivalence to
an alternative approach involving an artificial market consisting of after-tax
and after-expense assets, and we establish a type of consistency with classic
risk-minimization. Finally, a case study involving classic multi-state life
insurance payments in combination with a bond market exemplifies the results.
