A Benchmark Framework for Risk Management

The paper describes a general framework for contingent claim valuation for finance, insurance and general risk management. It considers security prices and portfolios with finite expected returns, where the growth optimal portfolio is taken as numeraire or benchmark. Benchmarked nonnegative wealth processes are shown to be supermartingales. Fair benchmarked values are conditional expectations of future benchmarked prices under the real world probability measure. Standard risk neutral and actuarial pricing formulas are obtained as special cases of fair pricing. The proposed benchmark framework covers the infinite time horizon and does not require the existence of an equivalent risk neutral pricing measure.