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.

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 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 method for generating a program for hedging guaranteed benefits of a set of variable annuity (VA) contracts, including automatically generating interpreted and compiled contract value projection code; generating vectorized integrated scenario sets including arbitrage-free interest rate, hedging instrument, and VA fund values based on financial market data and regression and cointegration analysis of the VA funds and user-selected hedging instruments; multi-threaded vectorized calculating of present value PVGij of projected VA benefit guarantee cash flows for each VA contract i for each vectorized integrated scenario set j; calculating of differences of PVGij to determine sensitivities to financial parameters (“Greeks”) for each contract; calculating of present value PVAij of projected asset cash flows for each asset i for each vectorized integrated scenario set j; calculating of differences of PVAij to determine sensitivities to financial parameters (“Greeks”) for each asset; and, presenting

Abstract: A computer-based method for determining a value of an index-offset deposit product, having a principal amount P, a term T, a specified guaranteed amount G, and an index credit C, comprising: d) setting trial values for fixed-income-linked crediting parameters for said product implying an expected fixed-income-linked credit component F at the end of the term T; e) determining a cost for an equity option paying equity-linked credit component E such that the index credit C=E+F, to be paid at T, together with the principal P, is at least equal to G; and f) summing said equity option cost, present value of principal, and present value of fixed-income-linked credit component to determine said value of said index-offset deposit product.

Abstract: A computer-based method, system and apparatus for pricing a tax flow-through annuity product. The resulting product is superior to traditional VA's, offering: lifetime income guarantees; capital gains tax treatment on annuity withdrawals; stock dividends taxed as dividends, not ordinary income; ETF-like tax efficiency by minimizing capital gains distributions, even on actively-managed funds; and wealth transfer efficiency through step-up in basis on death. The product benefits life insurance carriers and distributors. Investor benefits include: the ability to realize the full benefit of recent tax reform; the potential for better tax treatment than existing mutual funds; a guarantee of lifetime income; and the ability to pass assets on to heirs efficiently.

Abstract: A computer-based method for determining a value of an index-offset deposit product, having a principal amount P, a term T, a specified guaranteed amount G, and an index credit C, comprising: d) setting trial values for fixed-income-linked crediting parameters for said product implying an expected fixed-income-linked credit component F at the end of the term T; e) determining a cost for an equity option paying equity-linked credit component E such that the index credit C=E+F, to be paid at T, together with the principal P, is at least equal to G; and f) summing said equity option cost, present value of principal, and present value of fixed-income-linked credit component to determine said value of said index-offset deposit product.

Abstract: A computer-based method for determining a value of an index-offset deposit product, having a principal amount P, a term T, a specified guaranteed amount G, and an index credit C, comprising: d) setting trial values for fixed-income-linked crediting parameters for said product implying an expected fixed-income-linked credit component F at the end of the term T; e) determining a cost for an equity option paying equity-linked credit component E such that the index credit C=E+F, to be paid at T, together with the principal P, is at least equal to G; and f) summing said equity option cost, present value of principal, and present value of fixed-income-linked credit component to determine said value of said index-offset deposit product.

Abstract: A computer-based system for valuing a customized indexed call option.

Abstract: A quartz crystal sensor cell in which the sensor is secured to the base of a well defining a test sample space by a layer of adhesive between the respective peripheral surfaces. Also a quartz crystal sensor cell is provided in which the quartz sensor crystal is inclined relative to the opposite surface of the test sample space. These constructions respectively improve distinctness of the “Q” peak and problems from reflected waves in the space.

Abstract: An analytical apparatus, such as a quartz crystal microbalance, comprises a piezoelectric sensor and an oscillator circuit, coupled to the sensor, to oscillate at a frequency substantially determined by a resonant frequency of the sensor, and to provide an output signal at the oscillator frequency at an output. The oscillator circuit maintains a substantially constant drive signal to the piezoelectric sensor by an AGC (33) within a feedback loop of the oscillator. The gain control signal is used as an indication of the Q of the piezoelectric sensor. The drive signal to the sensor is made substantially sinusoidal by ensuring that all the elements in the feedback loop providing signal gain and attenuation are configured to operate in a substantially linear mode.

Abstract: An analytical apparatus, such as a quartz crystal microbalance, comprising a piezoelectric sensor and an oscillator circuit, coupled to the sensor, to oscillate at a frequency substantially determined by a resonant frequency of the sensor, and to provide an output signal at the oscillator frequency at an output, the oscillator circuit incorporates means to maintain a substantially constant drive signal to the piezoelectric sensor. Preferably the substantially constant drive signal is maintained by AGC means (33) within a feedback loop of the oscillator. Advantageously the gain control signal is used as an indication of the Q of the piezoelectric sensor. It is desirable that the drive signal to the sensor is substantially sinusoidal since this provides greater accuracy, sensitivity and stability for the apparatus. This can be achieved by ensuring that all the elements in the feedback loop providing signal gain and attenuation are configured to operate in a substantially linear mode.

Abstract: A quartz crystal sensor cell in which the sensor is secured to the base of a well defining a test sample space by a layer of adhesive between the respective peripheral surfaces. Also a quartz crystal sensor cell is provided in which the quartz sensor crystal is inclined relative to the opposite surface of the test sample space. These constructions respectively improve distinctness of the “Q” peak and problems from reflected waves in the space.

Abstract: An analytical apparatus, such as a quartz crystal microbalance, comprising a piezoelectric sensor and an oscillator circuit, coupled to the sensor, to oscillate at a frequency substantially determined by a resonant frequency of the sensor, and to provide an output signal at the oscillator frequency at an output, the oscillator circuit incorporates means to maintain a substantially constant drive signal to the piezoelectric sensor. Preferably the substantially constant drive signal is maintained by AGC means (33) within a feedback loop of the oscillator. Advantageously the gain control signal is used as an indication of the Q of the piezoelectric sensor. It is desirable that the drive signal to the sensor is substantially sinusoidal since this provides greater accuracy, sensitivity and stability for the apparatus. This can be achieved by ensuring that all the elements in the feedback loop providing signal gain and attenuation are configured to operate in a substantially linear mode.

Abstract: A computer-based system for hedging and pricing customized basket exchange swaps including a computer-based method for efficiently determining an asset mix to hedge a customized basket exchange swap with a specified term, notional amount, reference index, and custom index, and an estimated tracking error for the asset mix, comprising the steps of, updating a matrix factorization to reflect current financial market data, calculating an objective vector based on current composition of the custom index, determining a correlation coefficient and the asset mix from the matrix factorization and the objective vector, and, calculating an estimated tracking error from the correlation coefficient.

Abstract: A device for separating polymeric beads from a suspension of such beads comprising a flow cell through which the suspension of beads flows, and a radiation source which the stream of beads crosses. A detector detects the presence of a bead in the flow cell and control means directs the bead to a bead outlet channel.