Abstract
The minimization of the probability of ruin is a crucial criterion for determining the effect of the form of reinsurance on the wealth of the cedant and is a very important factor in choosing optimal reinsurance. However, this optimization criterion alone does not generally lead to a rational decision to choose an optimal reinsurance plan. This criterion acts only on the risk (minimizing it via the probability of ruin), but does not affect the technical benefit, that is to say, the insurer should not choose the optimal reinsurance treaty, it is not beneficial.We propose a new reinsurance optimization strategy that maximizes the technical benefit of an insurance company while maintaining a minimal level for the probability of ruin. The objective is to optimize with precision and ease of computation using Genetic algorithms.
Highlights
The objective of reinsurance differs from one insurer to another insofar as an insurer can choose reinsurance to minimize the variance of its technical profit (De Finetti [21]), or minimize risk measures, such as Value-at-Risk (VaR) and Conditional Tail Expectation (CTE) (Cai & Tan [17]), while another insurer chooses reinsurance which allows it to minimize its probability of ruin (Schmidli [47])
In this paper we propose a new reinsurance optimization strategy that maximizes the technical benefit of an insurance company while maintaining a minimal level for the probability of ruin, using Genetic algorithms Davis.L [20]. the latter, contrary to the deterministic methods, use only the value of the studied function, not its derivative nor any other auxiliary knowledge, which makes it easier to implement their effectiveness for more complex optimization problems
The organization of this paper is as follows: in the second section, we start with a preliminary, in the third section, we formulate our optimization problem for the different cases of reinsurance treaties, we propose the optimization procedure by the Augmented Lagrangian method and the Genetic Algorithms
Summary
The objective of reinsurance differs from one insurer to another insofar as an insurer can choose reinsurance to minimize the variance of its technical profit (De Finetti [21]), or minimize risk measures, such as Value-at-Risk (VaR) and Conditional Tail Expectation (CTE) (Cai & Tan [17]), while another insurer chooses reinsurance which allows it to minimize its probability of ruin (Schmidli [47]). It must refer to a new method that acts on minimizing the probability of ruin and maximizing the technical benefit, both at the same time, by seeking both optimal reinsurance treaty parameters and adjustment factors that maximize the technical benefit and minimize the risk of an insurance company. It must refer to a new method that acts on the minimization of the probability of ruin (by maximizing the adjustment coefficient) and on maximizing the technical benefit both at the same time and by seeking the parameters of the reinsurance treaties and the optimal adjustment coefficient; which maximize the technical benefit and minimize the risk of an insurance company at the same time. In the last section, we illustrate our model of optimization by a sample application
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