Statistical Estimation for Optimal Dividend Barrier Seminar

We consider a problem where an insurance portfolio is used to provide dividend income for the insurance company's shareholders. This is the apprication of ruin theory. Whenever the surplus attains the level ``barrier'', the premium income is paid to shareholders as dividends until the next claim occurs. We consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy and discuss the problem of the estimation of the optimal dividend barrier. Optimal dividend barrier is defined as the level of the barrier that maximizes the expectation of the discounted dividends until ruin. A dividends problem of ruin theory was initially proposed by [De Finetti, 1957] in the discrete time model. Thereafter [Buhlmann, 1970] discussed this problem in the classical risk model and lay the foundation. We discuss the problem of the estimation of the optimal dividend barrier, which is not sufficiently discussed so far. We construct the estimator of the expectation of the discounted dividends and the optimal dividend barrier, and show its consistency.