Abstract:
The problem of designing an optimal insurance strategy in a new multistep insurance model is investigated. This model introduces stepwise probabilistic constraints (Value-at-Risk constraints) on the insurer's capital, i.e., probabilistic constraints on the insurer's capital increments during one step. As the objective functional the mathematical expectation of the insurer's final capital is used. The total damage to the insurer at each step is modeled by the Gaussian distribution with parameters depending on a risk sharing function selected. In contrast to traditional dynamic optimization models for insurance strategies, the approach proposed below takes into account stepwise constraints; within this approach, the Bellman functions are constructed (and hence the optimal risk sharing is found) by simply solving a sequence of static insurance optimization problems. It is demonstrated that the optimal risk sharing is the so-called stop-loss insurance.
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