Liability Driven Investments under a Benchmark Based Approach

In this paper, we present an alternative approach as a suitable framework under which liability driven investments can be valued and hedged. This benchmark approach values both assets and liabilities consistently under the real world probability measure using the best performing portfolio, the growth optimal portfolio, as benchmark and numeraire. The benchmark approach identifies the investment strategy which is replicating a given claim at minimal cost. Should the liability under consideration be subject to nonhedgeable risk, e.g. mortality risk, benchmarked risk minimization identifies with its real world pricing formula the investment strategy which minimizes in a practical sense the price of a given claim and minimizes the benchmarked profit and loss from hedging. The application of the approach will be demonstrated for pensions. A least expensive pension scheme will be described that allows one in a fair and transparent manner to hedge in the least expensive way with minimal risk the post retirement payments for its members.