This invention provides methods and systems for trading and investing in groups of demand-based adjustable-return contingent claims, and for establishing markets and exchanges for such claims. (FIG. 2, item 262, 263, 264, 265) The advantages of the present invention, as applied to the derivative securities and similar financial markets, include increased liquidity, reduced credit risk, improved information aggregation, increased price transparency, reduced settlement or clearing costs, reduced hedging costs, reduced model risk, reduced event risk, increased liquidity incentives, improved self-consistency, reduced influence by market makers, and increased ability to generate and replicate arbitrary payout distributions. In addition to the trading of derivative securities, the present invention also facilitates the trading of other financial-related contingent claims; non-financial-related contingent claims such as energy, commodity, and weather derivatives; traditional insurance and reinsurance contracts; and contingent claims relating to events which have generally not been readily insurable or hedgeable such as corporate earnings announcements, future semiconductor demand, and changes in technology.