Insurance risk analysis with credit and debit interest

公司盈余的经典风险模型通常假设盈余为正值时，公司盈余不产生利息收入；当盈余为负时，不会借钱；即使盈余非常高，也不会向股东支付股息；保费收入是时间的确定性函数。近年来，保险风险分析的进展已将经济和金融条件考虑在内。特别是将利率和股息纳入风险分析的效果越来越受到人们的关注。在这个项目中，我们假设当公司盈余为正值时，盈余可以获得信贷利率的利息收入。当盈余为负时，公司可以借记利率借钱继续经营业务。盈余第一次为负的时候称为破产时间，破产就说发生在这个时刻。在破产之后，盈余可能会恢复到正水平。然而，由于债务的利息支付，如果负债过大，恢复盈利可能是不可能的。在这种情况下，据说会发生绝对的毁灭。我们假设公司可以根据股利策略向股东支付股利。此外，我们将讨论保险和金融风险相互依赖的情况。本课题将建立随机溢价收益的广义风险模型，研究存在借贷利息时的破产问题和最优股利策略。本研究将揭示借贷利息对破产、绝对破产和最优股利策略的影响。预期的结果将为破产，股息，投资以及保险风险和金融风险的依赖之间的相互作用提供新的见解。

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.