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The chain-ladder or development [1] method is a prominent [2] [3] actuarial loss reserving technique. The chain-ladder method is used in both the property and casualty [1] [4] and health insurance [5] fields. Its intent is to estimate incurred but not reported claims and project ultimate loss amounts. [5]
It is primarily used in the property and casualty [5] [9] and health insurance [2] fields. Generally considered a blend of the chain-ladder and expected claims loss reserving methods, [2] [8] [10] the Bornhuetter–Ferguson method uses both reported or paid losses as well as an a priori expected loss ratio to arrive at an ultimate loss estimate.
Ultimate loss amounts are necessary for determining an insurance company's carried reserves. They are also useful for determining adequate insurance premiums, when loss experience is used as a rating factor [4] [5] [6] Loss development factors are used in all triangular methods of loss reserving, [7] such as the chain-ladder method.
In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also utility function) in a form suitable for optimization — the problem that Ragnar Frisch has highlighted in his Nobel Prize lecture. [4]
Loss given default or LGD is the share of an asset that is lost if a borrower defaults. It is a common parameter in risk models and also a parameter used in the calculation of economic capital , expected loss or regulatory capital under Basel II for a banking institution .
In Python, the function cholesky from the numpy.linalg module performs Cholesky decomposition. In Matlab, the chol function gives the Cholesky decomposition. Note that chol uses the upper triangular factor of the input matrix by default, i.e. it computes = where is upper triangular. A flag can be passed to use the lower triangular factor instead.
In machine learning and mathematical optimization, loss functions for classification are computationally feasible loss functions representing the price paid for inaccuracy of predictions in classification problems (problems of identifying which category a particular observation belongs to). [1]
Note that this factor is "constant" in the sense that it is not a function of Y i, which is the variable over which the probability distribution is defined. However, it is definitely not constant with respect to the explanatory variables, or crucially, with respect to the unknown regression coefficients β k , which we will need to determine ...