On cash flows dependent on investment returns in life and pension insurance

On cash flows dependent on investment returns in life and pension insurance

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Speakers: Kristian Buchardt, Thomas Møller

We consider the problem of valuation and hedging of cash flows in life and pension insurance, where the cash flows can be dependent on the investment returns in a certain way. Examples of such cash flows are tax payments and investment costs. We consider contracts with a possibly stochastic benefit payment process, in a set-up where taxes and investment costs incur. The taxes and investment costs are specified as affine functions of the investment returns that is generated by the hedging strategy. The market consistent value of the combined contractual payments thus depends on the investment returns, and we show valuation and hedging results in both complete and incomplete markets. We decompose the market value into the benefit part, the tax part and the investment cost part, and determine the associated hedging strategies. In particular, we identify the (interest rate dependent) expected cash flows for the future tax payments and investment costs. The results are studied in the special case of affine interest rates, where some explicit results can be obtained. In the last part of the talk, we study numeric results. In particular, the results are compared with simpler approximating formulae that are based on an affine transformation of the forward interest rate.

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