Scholarlink

<p>Reinsurance treaties are one of the main instruments used by insurance companies for reducing their risks and balancing their technical performance. The selection of Pareto-efficient reinsurance strategies under Solvency II involves a computationally intensive multi-objective optimization problem with mixed continuous and discrete variables. Traditional simulation-based methods, like grid-search or random search, often become intractable due to the high-dimensional search space and the cost of extensive simulations. While evolutionary algorithms are typically able to solve these problems, their computational cost often prohibits real-time decision-making and sensitivity analysis. In this paper, we propose a novel deep learning architecture that formulates the optimization task as an inverse design problem. Our framework couples a proxy network, acting as a differentiable surrogate for the insurer’s internal model, with a generator network that directly maps target profitability levels to optimal reinsurance structures. We employ Gumbel-Softmax relaxation to effectively optimize discrete treaty features, such as the reinsurance selection based on its credit quality step, within a fully differentiable pipeline. We introduce a deep active learning loop that iteratively refines the model’s accuracy in the Pareto-optimal region, minimizing the required simulation budget. We validate the framework through a numerical application on a multi-line non-life insurer calibrated to the Italian market, aiming to jointly maximize the Return on Equity and Solvency Ratio. Our results demonstrate that the proposed approach outperforms traditional simulation-based methods in terms of frontier determination. Moreover, it achieves statistical equivalence with the evolutionary benchmark, Non-Dominated Sorting Genetic Algorithm II&#xa0;(NSGA-II), while reducing the computational budget by approximately 75%. Furthermore, the generator network reveals the continuous functional relationship between financial targets and treaty parameters, offering interpretable insights into the optimal risk transfer structure that discrete optimization methods fail to provide. This offers a novel perspective, which proves particularly valuable when dealing with a high number of potential combinations defining each strategy, effectively enabling real-time sensitivity analysis.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Multi-objective reinsurance optimization under Solvency II: an inverse design approach via deep learning

  • 期刊论文

  • 发表日期：

    2026年7月18日

查看全文
  • Matteo Crisafulli

摘要

Reinsurance treaties are one of the main instruments used by insurance companies for reducing their risks and balancing their technical performance. The selection of Pareto-efficient reinsurance strategies under Solvency II involves a computationally intensive multi-objective optimization problem with mixed continuous and discrete variables. Traditional simulation-based methods, like grid-search or random search, often become intractable due to the high-dimensional search space and the cost of extensive simulations. While evolutionary algorithms are typically able to solve these problems, their computational cost often prohibits real-time decision-making and sensitivity analysis. In this paper, we propose a novel deep learning architecture that formulates the optimization task as an inverse design problem. Our framework couples a proxy network, acting as a differentiable surrogate for the insurer’s internal model, with a generator network that directly maps target profitability levels to optimal reinsurance structures. We employ Gumbel-Softmax relaxation to effectively optimize discrete treaty features, such as the reinsurance selection based on its credit quality step, within a fully differentiable pipeline. We introduce a deep active learning loop that iteratively refines the model’s accuracy in the Pareto-optimal region, minimizing the required simulation budget. We validate the framework through a numerical application on a multi-line non-life insurer calibrated to the Italian market, aiming to jointly maximize the Return on Equity and Solvency Ratio. Our results demonstrate that the proposed approach outperforms traditional simulation-based methods in terms of frontier determination. Moreover, it achieves statistical equivalence with the evolutionary benchmark, Non-Dominated Sorting Genetic Algorithm II (NSGA-II), while reducing the computational budget by approximately 75%. Furthermore, the generator network reveals the continuous functional relationship between financial targets and treaty parameters, offering interpretable insights into the optimal risk transfer structure that discrete optimization methods fail to provide. This offers a novel perspective, which proves particularly valuable when dealing with a high number of potential combinations defining each strategy, effectively enabling real-time sensitivity analysis.