求償頻率與幅度風險下產物保險契約之評價

The Valuation of Property-Liability Insurance Contract under Frequency and Severity Risk

丘駿飛(Jiun-Fei Chiou) ； 劉維琪(Victor W. Liu) ； 吳欽杉(Chin-Shun Wu)

《中國財務學刊》 4卷1期 (1996/07) Pp. 49-82

https://doi.org/10.6545/JoFS.1996.4(1).3

摘要

為管制產物保險契約價格之訂定，本文根據應變求償權評價理論，發展保險契約之定價公式，期使保險定價達於公平。本文首先建構一般性評價模式，其中考慮了保險涵蓋期間內產生之保險金與投資所得所構成的現金流量。而各種風險將影響保險金與投資所得之變動所依循的隨機過程。其次，為獲取一具體之定價公式，本文考慮保險公司在面對求償頻率與幅度風險之特定情況，然後由此推導出一包含保險金之跳動的定價公式。結果顯示：保險金相對於投資所得之比值，將影響保險契約之價格。再者，保險金之跳動將使保險公司之資產與負債皆受到鉅幅衝擊。因此，保險契約之價格亦將隨之劇增。

關鍵字

產物保險契約 ； 應變求償權 ； 求償頻率與幅度風險 ； 隨機過程 ； 跳動

並列摘要

In order to regulate the pricing of property-liability insurance contracts, this study, based on the theory of contingent claim valuation, develops the insurance pricing formulas, which will lead to fair insurance pricing. Firstly, this study constructs a general valuation model for property-liability insurance contracts, which takes into account the cash flows consisting of both the claim indemnity and the investment income incurred during the insurance coverage period. Various risks will influence the stochastic processes followed by the claim indemnity and investment income, respectively. Secondly, to obtain a closed form solution of the pricing formula, this study considers the specific case in which the insurer confronts with the frequency and severity risk, and thence derives a pricing formula, into which the jumps incurred in claim indemnity are considered. The results show that the pricing of property-liability insurance contracts will depend on the ratio of the claim indemnity relative to the investment income. Furthermore, the jump's incurred in claim indemnity will exert significant impact upon both the assets and liabilities of the insurer. Hence, the price of property-liability insurance contracts will also increase drastically with these jumps.

並列關鍵字

Proper-Liability Insurance Contract ； Contingent Claim ； Frequency and Severity Risk ； Stochastic Process ； Jump