Abstract: An apparatus including: a processor configured to obtain asset return data for assets in a portfolio; populate initial estimated portfolio covariance matrix; compute initial portfolio weights for the assets; obtain respective amount of the assets according to the weights; populate an updateable matrix decomposition using the estimated portfolio covariance matrix and a scaling factor limiting respective degrees of negativity for the weights; obtain an update to the asset return data; update the updateable matrix decomposition according to the update; modify the weights using the updated matrix decomposition; and modify the assets in the portfolio according to the modified respective weights by purchasing or selling an additional quantity of an asset included in the portfolio to increase an amount of the asset included in the portfolio or selling a portion an asset included in the portfolio to decrease an amount of the asset included in the portfolio.

Abstract: A computer-based method for construction portfolios, including: populate an initial estimated portfolio covariance matrix; generate initial configurations by populating covariance matrices with randomly selected assets; determine scores for the initial configurations; calculate a first statistical function for the scores; select an initial configuration satisfying a criterion regarding the statistical function; generate iteration configurations by successively replacing one asset with a randomly selected asset; determining a score for each iteration configuration; calculate a second statistical function of the scores; calculate a statistical function of the first and second statistical functions; select a starting cooled configuration; generate modified cooled configurations by replacing one asset when a score for the modified cooled configuration satisfies a criterion; and when a score for a modified cooled configuration satisfies a criterion, save, in a memory unit, the assets and weights of dividend factor

Abstract: A computer-based system including: a memory unit configured to store computer readable instructions, path-dependent behavioral assumptions, and economic variables; and a processor configured to execute the computer readable instructions to perform a vectorized adjoint differentiation forward pass including: generating a full or pruned directed acyclic graph (DAG) representation of a procedure for computation of the behaviorally path-dependent value for the financial product; computing, using the DAG representation, the behaviorally path-dependent value for the financial product; and performing an adjoint differentiation backward pass on said full or pruned DAG representation to obtain a result.

Abstract: A computer-based method for determining a value of an index-offset deposit product, having a principal amount, a term, a specified guaranteed amount, and an index credit comprising the step of setting trial values for fixed-income-linked crediting parameters for the product implying an expected fixed-income-linked credit component at the end of the term. The method further comprises the steps of determining a cost for an option paying an index-linked credit component such that a composite index credit together with the principal is at least equal to a specified guaranteed amount.

Abstract: A computer-based apparatus for representing and acting on an indexed reversionary annuity, including a memory unit for at least one specially programmed computer configured to store computer readable instructions and an initial income amount, and a processor for the at least one specially programmed computer configured to execute the computer readable instructions to determine a set of indexing parameters P and generate an updated income amount at an end of a specified indexing term T based in part on performance of at least one index and the set of indexing parameters P.