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

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

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

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

Computation of bonus in multi-state life insurance

We consider computation of market values of bonus payments in multi-state with-profit life insurance. The bonus scheme consists of additional benefits bought according to a dividend strategy that depends on the past realization of financial risk, the current individual insurance risk, the number of additional benefits currently held, and so-called portfolio-wide means describing the shape of the insurance business. We formulate numerical procedures that efficiently combine simulation of financial risk with classic methods for the outstanding insurance risk. Special attention is given to the case where the number of additional benefits bought only depends on the financial risk. Methods and results are illustrated via a numerical example