Optimal Insurance Strategy Design in a Risk Process under Value-at-Risk Constraints on Capital Increments

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 ste...

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Bibliographic Details
Published in:Automation and remote control 2020-09, Vol.81 (9), p.1679-1691
Main Authors: Golubin, A. Yu, Gridin, V. N.
Format: Article
Language:English
Subjects:
639/301/1034/1035
639/925/357/995
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Constraint modelling
Control
Control in Social Economic Systems
Gaussian distribution
Insurance
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Normal distribution
Optimization
Risk sharing
Robotics
Statistical analysis
Systems Theory
Citations: Items that this one cites
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Summary: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.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117920090076