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 – in a certain sense – 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.

中文翻译：

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保险支付流程的税收和费用修正风险最小化

我们研究了在存在税收和费用的情况下为保险支付过程确定风险最小化投资策略的问题。我们考虑税收和费用连续和对称支付的情况，并引入税收和费用修正风险最小化的概念。在存在税收和费用的情况下，风险最小化策略被推导出并与与原始支付流程的修改版本相关的 Galtchouk-Kunita-Watanabe 分解相关联。此外，我们展示了与涉及由税后和费用后资产组成的人工市场的替代方法的等效性，并且我们在某种意义上建立了与经典风险最小化的一致性。最后，