The Determination of Fair Profits for the Property‐Liability Insurance Firm
构建了连续时间下的单期和动态估值模型，用于确定财产责任保险合同的公平保费和承保利润，模型假设索赔频率和价格指数受多变量维纳过程影响。
ABSTRACT Single period and dynamic valuation models in continuous time, under certainty and uncertainty, are developed for a property‐liability insurance contract to determine the “fair” (competitive) premium and underwriting profit. The intertemporal stochastic model assumes that the claim frequency and the price index of claim settlements are functions of a set of underlying state variables which follow a multivariate Wiener process. The competitive premium is shown to be proportional to the claim frequency and the price index for claim settlements at the time the policy is issued. The factor of proportionality varies directly with the claim settlement rate and the length of coverage, and inversely with the risk‐adjusted real interest rate on the dollar‐valued claim rate.