Abstract:
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.
