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.

Abstract: A method and apparatus for determining an optimal replicating portfolio for a given target portfolio involves an initial step wherein a user defines a target portfolio to be replicated, a set of available market instruments from which the replicating portfolio may be created, a set of future scenarios, a horizon date, and a minimum profit to be attained. A representation of the trade-off between risk and expected profit for some arbitrary replicating portfolio is then determined and used to calculate a maximum risk-adjusted profit. The maximum risk-adjusted profit reflects that level of return that may be achieved with an optimum degree of risk; that is, it reflects that point in the risk/reward trade-off where a marginal cost of risk is equivalent to a marginal benefit attainable by assuming that risk. The method then uses the predefined set of available market instruments to identify a set of transactions that will create a replicating portfolio that will achieve the maximum risk-adjusted profit.

Abstract: A method and apparatus are provided for optimally allocating available resources in a physical system defined by a mathematical model having parameters of uncertain values. The method comprises the steps of firstly assigning a value to each of the uncertain parameters in the mathematical model based on a scenario that may or is expected to occur. Thereafter, given the parameter values at each possible scenario, the mathematical model is solved to yield the best solution of the mathematical model for that scenario. Once this has been complete, a probability value representing the expected probability that the scenario will occur is assigned to each scenario solution. The scenario parameter values, scenario solutions and scenario probabilities are then used to determine a single solution to the mathematical model which best "fits" the desired system behavior under the uncertainty defined by all of the scenarios considered. The single solution is then used to allocate the resources in the system.