This invention provides methods and systems for trading and investing in groups of demand-based adjustable return ("DBAR") contingent claims, including digital options, and for establishing markets and exchanges for such claims. The advantages of the present invention, as applied to the establishment and operation of a DBAR digital options exchange, include the ability to offer investments whose profit and loss scenarios are comparable to those for digital options or other derivatives in traditional securities markets, without the need for options or derivatives sellers or order-matching of conventional markets. A DBAR digital options exchange of the present invention can also offer conditional investments, or limit orders, in which an investment in a state of a DBAR contingent claim (such as the price of an underlying asset or index) can be executed or withdrawn in response to the implied probability of the occurrence of that state.