Axiom of solvency and portfolio immunization under random interest rates

The paper concerns the interest rate risk management of insurance companies. It is assumed that assets and liabilities are stochastic processes and that regulatory demands on solvency are satisfied under the basic TSIR. Lower bounds on change in the portfolio present value are established when the interest rates change randomly. The bounds may be used to immunize the portfolio valuation when arbitrary changes of the interest rate scenarios are considered. An application to construct an optimal funding method for defined benefit pension plans is discussed in detail. In particular, a theoretical background is provided for the following conservative long-term strategy for the interest rate risk management: (1) assume a pessimistic (i.e. relatively low) interest rate scenario to discount cash flows of both assets and liabilities; (2) under this term structure of interest rates arrange the accumulated net assets cash flow to be the smallest concave majorant of accumulated liability cash flow. It is shown that this strategy is quite likely to give a positive change in the portfolio surplus in response to changing the future interest rate scenario. What is more, it leads to the least possible decrease of the portfolio net worth in the least favorable circumstances. A further improvement of this strategy is proposed.