Abstract:
This paper considers a market containing both continuous and discrete noise. Modest
assumptions ensure the existence of a growth optimal portfolio. Non-negative self financing
trading strategies, when benchmarked by this portfolio, are local martingales
under the real-world measure. This justifies the fair pricing approach, which expresses
derivative prices in terms of real-world conditional expectations of benchmarked payoffs.
Two models for benchmarked primary security accounts are presented, and fair
pricing formulas for some common contingent claims are derived.
