Journal of the
Korean Mathematical Society JKMS

The paper studies the evolution of the financial markets and pays the basic attention to the role of financial innovations (derivative securities) in this process. A characterization of both complete and incomplete markets is given through an identification of the sets of contingent claims and terminal wealths of self-financing portfolios. The dynamics of the financial system is described as a movement of incomplete markets to a complete one when the volume of financial innovations is growing up and the spread tends to zero (the Merton financial innovation spiral). Namely in this context the paper deals with the problem of pricing risks in both field: finance and insurance.

Keywords: derivative securities, financial innovations, complete and incomplete markets, martingales, martingale measures, risks, Merton's financial innovation spiral

MSC numbers: G10, G13, G22