Abstract: An improved method uses quantum processing devices to determine optimal sets of bids in combinatorial auctions. In one approach, a list of bids is received. Each bid specifies a price for a package of one or more items offered in the auction. The bids may be conflicting. An objective function based on the list of bids is formulated. The objective function has a form suitable for solution by a quantum processing device, which is used to optimize the objective function, thereby determining which bids are accepted.

Abstract: An improved method uses quantum processing devices to optimize a portfolio of financial assets. In one approach, a list of lots available for purchase is received. Each lot specifies financial assets included in the lot and a price to purchase the lot. A budget for the portfolio is also received. An objective function is formulated based on the list of lots and on the budget. The objective function has a form suitable for solution by a quantum processing device, which is used to optimize the objective function, thereby determining which lots are to be purchased.

Abstract: A method and apparatus for developing a structural model of credit risk that incorporates the short-term uncertainty inherent in default events is disclosed. The model is based on the assumption of incomplete information, taking as premise that bond investors are not certain about the true level of a firm's value that may trigger default. In addition, the coherent integration of structure and uncertainty is facilitated with compensators. Compensators form the infrastructure of a class of credit models that is broad enough to include traditional structural models, intensity-based models, and a great deal more. Several empirical examples are provided that compare default probabilities and credit yield spreads forecast by the incomplete information model to the output of a Black and Cox (1976) model. It is found that the incomplete information model reacts more quickly and, unlike traditional structural models, forecasts positive short-term credit spreads for firms that are in distress.

Abstract: A method and apparatus for developing a structural model of credit risk that incorporates the short-term uncertainty inherent in default events is disclosed. The model is based on the assumption of incomplete information, taking as premise that bond investors are not certain about the true level of a firm's value that may trigger default. In addition, the coherent integration of structure and uncertainty is facilitated with compensators. Compensators form the infrastructure of a class of credit models that is broad enough to include traditional structural models, intensity-based models, and a great deal more. Several empirical examples are provided that compare default probabilities and credit yield spreads forecast by the incomplete information model to the output of a Black and Cox (1976) model. It is found that the incomplete information model reacts more quickly and, unlike traditional structural models, forecasts positive short-term credit spreads for firms that are in distress.