An actuarial approach to option pricing under the physical measure and without market assumptions

As the title may indicate, this paper uses merely probabilistic and actuarial considerations for pricing options. There are no economical considerations involved, and our approach is valid even when an equilibrium price measure does not exist (arbitrage, non-equilibrium) or is not unique (incompleteness). We only make use of the physical measure that generates the pay-out distributions. The approach does not in general carry over to general derivative securities, since we use an interpretation of the securities under consideration as being potential losses or claims from the issuers point of view. Under this interpretation we calculate the price of the security as the fair premium needed to insure the potential loss. As a special case of our formula we derive the Black and Scholes formula.