Hedging and cash flows in the presence of taxes and expenses in life and pension insurance

In investment and insurance contracts, certain stipulated payments may depend on the hedging strategy. We study the problem of calculation, hedging and valuation of such cash flows, by considering a payment process in a setup with taxes and investment costs that are functions of the investment returns or the current value of the hedging strategy. We determine the market value of the combined liability and decompose the value into the tax part, the investment cost part and the benefit part, and we determine the associated hedging strategies. Moreover, we identify the expected future tax payments and investment cost cash flows. Our results show that the current Danish insurance accounting practice for taxes is in general conservative, when considered in an idealized setting with symmetric and continuously-paid taxes. Finally, we consider the special case of affine interest rates, where explicit results can be obtained, and study some numerical results.