Optimization techniques perform an important role in different domains of statistic. Examples of parameter estimation of different distributions, correlation analysis (parametric and nonparametric), regression analysis, optimal allocation of resources in partial research, exploration of response surfaces, design of experiments, efficiency tests, reliability theory, survival analysis are the most known methods of statistical analysis in which we find optimization techniques.
The paper contains a synthetic presentation of the main statistical methods using classical optimization techniques, numerical optimization methods, linear and nonlinear programming, variational calculus techniques. Also, an example of applying the “simplex” algorithm in making a decision to invest an amount on the stock exchange, using a prediction model..
The anticipation of the amount of the losses generated by natural disasters is of maximum importance for insurers. We present a method to determine insurance premiums for catastrophic risks. This method takes into account: statistical data reflected in the yearly average compensation index, an appropriate time period in which the insurance company retrieves the financial losses incurred by the payment of large compensations, the preventive setting up of a reserve fund of the insurer in order to cover partially the catastrophic risk, and a reinsurance strategy. All these are meant to keep up the level of the premiums within an interval of values such that they are still competitive or at least fairly good. In our scenario, we will consider the situation in which the insurer has to borrow money in order to be able to pay the damage claims that arise following a calamity, the loans being refunded in a certain number of years. We give numerical illustration.
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