Abstract
A new approach to the problem of approximate optimization of insurance business is proposed that lies in optimizing net income (dividends) under a constraint on the probability of ruin. The probability is then replaced by its exponential upper bound. This trick allows one to eliminate a complicated probabilistic constraint and to decompose the problem according to separate lines of business. Thus, problems of optimization of tariffs, insurance, portfolios, reinsurance treaties, and operational management are approximately solved.
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