Abstract: An apparatus includes a processor to: train a first neural network of a chain to generate first configuration data including first trained parameters, wherein the chain performs an analytical function generating a set of output values from a set of input values, each neural network has inputs to receive the set of input values and outputs to output a portion of the set of output values, and the neural networks are ordered from the first at the head to a last neural network at the tail, and are interconnected so that each neural network additionally receives the outputs of a preceding neural network; train, using the first configuration data, a next neural network in the chain ordering to generate next configuration data including next trained parameters; and use at least the first and next configuration data and data indicating the interconnections to instantiate the chain to perform the analytical function.

Abstract: An apparatus includes a processor to: train a first neural network of a chain to generate first configuration data including first trained parameters, wherein the chain performs an analytical function generating a set of output values from a set of input values, each neural network has inputs to receive the set of input values and outputs to output a portion of the set of output values, and the neural networks are ordered from the first at the head to a last neural network at the tail, and are interconnected so that each neural network additionally receives the outputs of a preceding neural network; train, using the first configuration data, a next neural network in the chain ordering to generate next configuration data including next trained parameters; and use at least the first and next configuration data and data indicating the interconnections to instantiate the chain to perform the analytical function.

Abstract: An apparatus includes a processor to: train a first neural network of a chain to generate first configuration data including first trained parameters, wherein the chain performs an analytical function generating a set of output values from a set of input values, each neural network has inputs to receive the set of input values and outputs to output a portion of the set of output values, and the neural networks are ordered from the first at the head to a last neural network at the tail, and are interconnected so that each neural network additionally receives the outputs of a preceding neural network; train, using the first configuration data, a next neural network in the chain ordering to generate next configuration data including next trained parameters; and use at least the first and next configuration data and data indicating the interconnections to instantiate the chain to perform the analytical function.

Abstract: An apparatus includes a processor to: train a first neural network of a chain to generate first configuration data including first trained parameters, wherein the chain performs an analytical function generating a set of output values from a set of input values, each neural network has inputs to receive the set of input values and outputs to output a portion of the set of output values, and the neural networks are ordered from the first at the head to a last neural network at the tail, and are interconnected so that each neural network additionally receives the outputs of a preceding neural network; train, using the first configuration data, a next neural network in the chain ordering to generate next configuration data including next trained parameters; and use at least the first and next configuration data and data indicating the interconnections to instantiate the chain to perform the analytical function.

Abstract: Systems and methods are provided for determining a loss mitigation reserve requirement based on a risk measure estimation and a confidence interval associated with the risk measure estimation. Distribution parameters of a frequency model and distribution parameters of a severity model are determined, and a covariance matrix representing the determined parameters of the distribution of the frequency model and the determined parameters of distribution of the severity model is generated. One or more analytical derivatives of a cumulative distribution function of the frequency model, one or more analytical derivatives of a cumulative distribution function of the severity model, and a parameter covariance matrix are calculated. A confidence interval is computed for the risk measure estimation based on a vector of derivatives of a cumulative distribution function.

Abstract: A method is provided for analyzing operational risk associated with one or more organizations, comprising receiving operational loss data from a plurality of organizations at a third-party risk management entity that is a separate entity from the plurality of organizations. The operational loss data includes confidential information regarding one or more of the plurality of organizations. The data received from the plurality of organizations, including the confidential information, is pooled. The pooled data is used to generate an operational risk model for one of the plurality of organizations, and this operational risk model is transmitted to the organization. A system for modeling operational risk for a plurality of organizations is provided, comprising a first data store configured to collect data regarding operational losses from the plurality of organizations, whose data includes confidential information regarding one or more of the organizations.

Abstract: Systems and methods are provided for determining a loss mitigation reserve requirement based on a risk measure estimation and a confidence interval associated with the risk measure estimation. Distribution parameters of a frequency model and distribution parameters of a severity model are determined, and a covariance matrix representing the determined parameters of the distribution of the frequency model and the determined parameters of distribution of the severity model is generated. One or more analytical derivatives of a cumulative distribution function of the frequency model, one or more analytical derivatives of a cumulative distribution function of the severity model, and a parameter covariance matrix are calculated. A confidence interval is computed for the risk measure estimation based on a vector of derivatives of a cumulative distribution function.