Abstract: A method for a quadratic program or quadratically constrained program stored in a non-transitory computer readable medium, includes receiving input for coefficients of a quadratic problem or a quadratically constrained problem by a computer for storage in the non-transitory computer readable medium, determining scaling factors by a processor by using the input in the quadratic program or quadratically constrained program configured for optimality conditions by considering a symmetric N×N matrix Q0 and/or Mq N×N matrices Qk in the transformation, where N is an integer and k=1, . . . , Mq is an integer, and outputting, by the computer, transformed coefficients of column scaling factor ?, row scaling factor ?, and right hand side scaling factor ?, where ?>0, ?>0 and ?>0.

Abstract: Systems and methods for generating an integrated market and credit loss distribution for the purpose of calculating one or more risk measures associated with a portfolio of instruments are disclosed. In at least one embodiment, compound risk factor sampling is performed that comprises conditionally generating multiple systemic credit driver samples for each market risk factor sample generated per time step of a simulation. There are also disclosed systems and methods for determining an optimal number of sample values for each of the market risk factors, systemic credit drivers, and optionally, idiosyncratic credit risk factors that would be required in order to obtain an acceptable amount of variability in the calculated risk estimates and/or to satisfy an available computational budget.

Abstract: Systems and methods for generating an integrated market and credit loss distribution for the purpose of calculating one or more risk measures associated with a portfolio of instruments are disclosed. In at least one embodiment, compound risk factor sampling is performed that comprises conditionally generating multiple systemic credit driver samples for each market risk factor sample generated per time step of a simulation. There are also disclosed systems and methods for determining an optimal number of sample values for each of the market risk factors, systemic credit drivers, and optionally, idiosyncratic credit risk factors that would be required in order to obtain an acceptable amount of variability in the calculated risk estimates and/or to satisfy an available computational budget.

Abstract: Systems and methods for generating an integrated market and credit loss distribution for the purpose of calculating one or more risk measures associated with a portfolio of instruments are disclosed. In at least one embodiment, compound risk factor sampling is performed that comprises conditionally generating multiple systemic credit driver samples for each market risk factor sample generated per time step of a simulation. There are also disclosed systems and methods for determining an optimal number of sample values for each of the market risk factors, systemic credit drivers, and optionally, idiosyncratic risk factors that would be required in order to obtain an acceptable amount of variability in the calculated risk estimates and/or to satisfy an available computational budget.

Abstract: Systems and methods for generating an integrated market and credit loss distribution for the purpose of calculating one or more risk measures associated with a portfolio of instruments are disclosed. In at least one embodiment, compound risk factor sampling is performed that comprises conditionally generating multiple systemic credit driver samples for each market risk factor sample generated per time step of a simulation. There are also disclosed systems and methods for determining an optimal number of sample values for each of the market risk factors, systemic credit drivers, and optionally, idiosyncratic risk factors that would be required in order to obtain an acceptable amount of variability in the calculated risk estimates and/or to satisfy an available computational budget.

Abstract: Systems and methods for generating an integrated market and credit loss distribution for the purpose of calculating one or more risk measures associated with a portfolio of instruments are disclosed. In at least one embodiment, compound risk factor sampling is performed that comprises conditionally generating multiple systemic credit driver samples for each market risk factor sample generated per time step of a simulation. There are also disclosed systems and methods for determining an optimal number of sample values for each of the market risk factors, systemic credit drivers, and optionally, idiosyncratic risk factors that would be required in order to obtain an acceptable amount of variability in the calculated risk estimates and/or to satisfy an available computational budget.

Abstract: A system and method for valuing a portfolio in terms of its performance relative to a specified benchmark under a range of future scenarios is disclosed. In particular, a portfolio is taken and two values related to the portfolio are calculated: the first value corresponding to an amount by which the value of the portfolio is expected to fall below the value of a benchmark over a given time horizon, and a second value corresponding to an amount by which the value of the portfolio is expected to exceed the value of a benchmark over a given time horizon, in view of the range of different future scenarios. Means for determining the portfolio which optimally trades-off these two values, and to evaluate risk/reward performance measures using these two values which can be used to rank instruments, securities or portfolios are disclosed. Means for pricing portfolio insurance for optimal portfolios are also disclosed.

Abstract: Systems and methods for generating an integrated market and credit loss distribution for the purpose of calculating one or more risk measures associated with a portfolio of instruments are disclosed. In at least one embodiment, compound risk factor sampling is performed that comprises conditionally generating multiple systemic credit driver samples for each market risk factor sample generated per time step of a simulation. There are also disclosed systems and methods for determining an optimal number of sample values for each of the market risk factors, systemic credit drivers, and optionally, idiosyncratic risk factors that would be required in order to obtain an acceptable amount of variability in the calculated risk estimates and/or to satisfy an available computational budget.

Abstract: A system and method for valuing a portfolio in terms of its performance relative to a specified benchmark under a range of future scenarios is disclosed. In particular, a portfolio is taken and two values related to the portfolio are calculated: the first value corresponding to an amount by which the value of the portfolio is expected to fall below the value of a benchmark over a given time horizon, and a second value corresponding to an amount by which the value of the portfolio is expected to exceed the value of a benchmark over a given time horizon, in view of the range of different future scenarios. Means for determining the portfolio which optimally trades-off these two values, and to evaluate risk/reward performance measures using these two values which can be used to rank instruments, securities or portfolios are disclosed. Means for pricing portfolio insurance for optimal portfolios are also disclosed.

Abstract: This invention relates to a system and method for valuing a portfolio in terms of its performance relative to a specified benchmark under a range of future scenarios. In particular, the invention takes a portfolio and calculates two values related to the portfolio: the first value corresponding to an amount by which the value of the portfolio is expected to fall below the value of a benchmark over a given time horizon, and a second value corresponding to an amount by which the value of the portfolio is expected to exceed the value of a benchmark over a given time horizon, in view of the range of different future scenarios. The invention provides a means for determining the portfolio which optimally trades-off these two values, and to evaluate risk/reward performance measures using these two values which can be used to rank instruments, securities or portfolios. The invention also provides a means for pricing portfolio insurance for optimal portfolios.