巨災風險下產險公司之盈餘價值

本文主要目的是將多數過去研究未包含之隨機破產風險以及連帶的破產成本列入考量，來求出在巨災風險下產險公司的合理盈餘價值，因為若未將提早破產及巨災風險列入評價模式，可能會造成盈餘價值高估，而如果忽略巨災風險中的系統風險成份更可能造成盈餘價值大幅地高估。我們的模式可顯示過去研究可能錯估的部份。文中分析還包含了在產險業常見的不同巨災衝擊分配，以及非系統性與系統性巨災風險的結果。在不同假設下我們可分別得出分析解與數值解，我們分析的結果有潛力可以取代傳統歐式選擇權而成為更切合實際的評價模式。

關鍵字

盈餘；清償不足；巨災；擴散過程

並列摘要

This paper develops the surplus valuation model for the property and liability insurer with the consideration of the random-time insolvency risk and the associated insolvency cost, which is not assumed in most previous studies. Traditional model may overestimate surplus value because early ruin risk and catastrophic risk are not included. The jump models under various distributions, which is commonly encountered by P/L insurer, are also investigated. The catastrophe risk is analyzed under systematic framework. We show that actual surplus value will be much lower if the associated catastrophe risk consists of systematic component. Under certain assumptions, we are able to derive the analytical solutions and the numerical solutions. Our result can be viewed as a potential advance from traditional option-based valuation model.