Insurance risk analysis with credit and debit interest

经典的公司盈余风险模型通常假设，当盈余为正时，盈余不会产生利息收入;当盈余为负时，不会借钱;即使盈余处于非常高的水平，也不会向股东支付股息;保费收入是时间的确定性函数。最近，保险风险分析的进展考虑到了经济和金融条件。特别是在风险分析中加入利率和股利的影响越来越受到人们的关注。在这个建议的项目中，我们假设，当一个公司的盈余是积极的，盈余可以赚取利息收入，在信贷利率。当盈余为负时，公司可以以借方利率借款以继续经营业务。盈余第一次为负的时刻称为破产时刻，而破产就发生在这一时刻。破产后，盈余可能会恢复到正的水平。然而，由于债务的利息支付，如果负债太大，就不可能恢复盈利。在这种情况下，绝对破产被称为发生。我们假设一家公司可能会根据股利策略向股东支付股利。此外，我们还讨论了保险风险与金融风险相依的情形.本计画将发展一些随机保费收入的广义风险模型，并研究在借贷利息存在下的破产问题与最适分红策略。本研究将揭示借贷利息对破产、绝对破产及最适股利策略之影响。预期的结果将提供新的见解破产，股息，投资的相互作用，以及保险风险和金融风险的依赖性。

The classical risk model for the surplus of a company usually assumes that no interest income will be earned on the surplus when the surplus is positive; no money will be borrowed when the surplus is negative; no dividends will be paid to shareholders even if the surplus is at a very high level; and  premium income is a deterministic function of time. Recently, advances in insurance risk analysis have taken into consideration economic and financial conditions. In particular, the effect of incorporating interest rates and dividends in risk analysis has attracted more and more attention. In this proposed project, we assume that when the surplus of a company is positive, the surplus may earn interest income at a rate of credit interest. When the surplus is negative, the company may borrow money at a rate of debit interest to continue running its business. The first time the surplus is negative is called the time of ruin, and ruin is said to occur at this moment. The surplus may return to a positive level after ruin. However, due to interest payments on debt, a return to profitability may be impossible if the liabilities are too great. In this situation, absolute ruin is said to occur. We assume that a company may pay dividends to shareholders according to dividend strategies. In addition, we will discuss the case when insurance and finance risk are dependent. The project will develop some generalized risk models for stochastic premium income and study ruin problems and optimal dividend strategies in the presence of credit and debit interest. This research will reveal the impact of credit and debit interest on ruin, absolute ruin, and optimal dividend strategies. The anticipated outcomes will provide new insights into the interplay of ruin, dividends, investments, and the dependence of insurance risk and finance risk.