An alternative axiomatic characterisation of pricing operators. (English) Zbl 1355.91080

Kassberger, Stefan; Liebmann, Thomas

J. Appl. Probab. 53, No. 4, 1257-1264 (2016).

Summary: In the spirit of the axiomatic approach by L. C. G. Rogers [“The origins of risk-neutral pricing and the Black-Scholes formula”, in: The handbook of risk management and analysis. Chichester: John Wiley. 81–94 (1998)] we show the equivalence between a set of assumptions on the behaviour of prices and the existence of a representation of these prices as conditional expectations. We rely on only weak assumptions and avoid any a priori modelling of negligible events or of any market filtration. Rather, both endogenously emerge along with the representation as conditional expectations.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
60G44	Martingales with continuous parameter
47A67	Representation theory of linear operators
47N20	Applications of operator theory to differential and integral equations

Keywords:

axiomatic characterisation; conditional expectation; martingale; pricing operator