Insurance risk analysis with credit and debit interest

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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.