# Tax- and expense-modified risk-minimization for insurance payment processes

## TL;DR

This paper develops a framework for risk-minimizing investment strategies in insurance payments considering continuous taxes and expenses, linking it to modified payment processes and artificial market models.

## Contribution

It introduces tax- and expense-modified risk-minimization, connecting it to Galtchouk-Kunita-Watanabe decompositions and artificial market models, extending classic risk-minimization theory.

## Key findings

- Derived risk-minimizing strategies accounting for taxes and expenses.
- Linked strategies to Galtchouk-Kunita-Watanabe decompositions.
- Demonstrated the approach with a multi-state life insurance case study.

## Abstract

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.