We propose a model that integrates investment, underwriting, and consumption/dividend policy decisions for a nonlife insurer by using a risk control variable related to the wealth-income ratio of the firm. This facilitates the efficient transfer of insurance risk to capital markets since it allows to select simultaneously investments and underwriting volume. The model is particularly valuable for business lines with significant exposure to extreme events and disaster risk, as it accounts for features usually depicted during negative economic shocks and catastrophic events, such as Levy-type jump-diffusion dynamics for the financial log-returns that are in turn correlated with insurance premiums and liabilities, as well as worst-case scenarios in which policyholders in the insurance portfolio report claims with the same severity simultaneously. Using the martingale method, we determine an optimal solvency threshold or wealth-income ratio, and investment strategy that maximizes the expected utility from dividend payouts that follows a (possibly stochastic) consumption clock. We illustrate the main results with numerical examples for log- and power-utility functions, and (bounded variation) tempered stable Levy jumps.

中文翻译：

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具有非寿险风险的 LEVY 型跳跃扩散模型中的投资组合分配

我们提出了一个模型，该模型通过使用与公司财富收入比率相关的风险控制变量，为非寿险公司整合投资、承保和消费/股息政策决策。这有助于将保险风险有效地转移到资本市场，因为它允许同时选择投资和承保量。该模型对于严重暴露于极端事件和灾难风险的业务线特别有价值，因为它解释了负面经济冲击和灾难性事件中通常描述的特征，例如财务对数回报的利维型跳跃扩散动力学反过来又与保险费和负债相关，以及保险组合中的保单持有人同时报告具有相同严重程度的索赔的最坏情况。使用鞅方法，我们确定最佳偿付能力阈值或财富收入比，以及根据（可能是随机的）消费时钟从股息支付中最大化预期效用的投资策略。我们通过对数和功率效用函数的数值示例以及（有界变化）回火稳定 Levy 跳跃来说明主要结果。