本文選題：鞅 + 破產(chǎn)概率　； 參考：《重慶理工大學(xué)》2013年碩士論文

【摘要】：在保險精算中，破產(chǎn)論是保險精算的重要組成部分，破產(chǎn)論研究的核心問題是通過破產(chǎn)概率這一量化的指標(biāo)來衡量保險公司的運營情況。破產(chǎn)概率是指保險公司盈余資金為負值的概率，破產(chǎn)概率可以作為保險公司風(fēng)險評估的依據(jù)，因此對保險公司和保險監(jiān)督部門有極為重要的指導(dǎo)作用。近幾年來，鞅作為一種有力的研究理論工具逐漸向各個學(xué)科領(lǐng)域滲透。借助鞅這個理論工具來研究保險精算中的風(fēng)險模型，具有很高的實用價值。 文章的研究內(nèi)容主要分為兩個部分： 第一，一般的破產(chǎn)理論中，處理盈余過程時常常未考慮利率的因素，或者是在常利率的條件下考慮破產(chǎn)概率問題。但事實上，，受外部經(jīng)濟因素的影響，隨機利率會更符合實際情況。本文討論的保險公司破產(chǎn)概率，是指在隨機利率的條件下，對離散的風(fēng)險模型，利用鞅論的方法得到最終破產(chǎn)概率的指數(shù)型上界。 第二，通過鞅論得到破產(chǎn)概率上界，保險人以破產(chǎn)概率為準(zhǔn)則，通過再保險策略使自身風(fēng)險達到最小值，通過更新過程來描述聚合風(fēng)險，破產(chǎn)概率的上界由調(diào)節(jié)系數(shù)給定，而這里的調(diào)節(jié)系數(shù)可視為超額損失再保險自留額的函數(shù)，通過對該函數(shù)的分析，得出針對保險人最優(yōu)的自留額，使得破產(chǎn)概率上界達到最小。
[Abstract]:In actuarial insurance, bankruptcy theory is an important part of actuarial insurance. The core problem of bankruptcy theory research is to measure the operation of insurance companies through the quantitative index of bankruptcy probability. The probability of bankruptcy is the probability that the surplus capital of insurance company is negative, and the probability of bankruptcy can be used as the basis of risk assessment of insurance company, so it plays an important role in guiding the insurance company and the insurance supervision department. In recent years, martingale, as a powerful theoretical tool, has gradually penetrated into various disciplines. It is of great practical value to study the risk model in actuarial insurance by means of martingale. The research content of this paper is divided into two parts: Firstly, in general bankruptcy theory, the factor of interest rate is often not taken into account when dealing with the surplus process, or the ruin probability is considered under the condition of constant interest rate. But in fact, the impact of external economic factors, random interest rates will be more in line with the actual situation. The ruin probability of insurance companies discussed in this paper is to obtain the exponential upper bound of the final ruin probability for discrete risk models under the condition of random interest rate by means of martingale theory. Secondly, the upper bound of ruin probability is obtained by martingale theory, the insurer takes ruin probability as the criterion, the risk is minimized by reinsurance strategy, and the aggregation risk is described by updating process. The upper bound of ruin probability is given by the adjustment coefficient. The adjustment coefficient can be regarded as a function of the retention amount of excess loss reinsurance. Through the analysis of the function, the optimal retention amount for the insurer is obtained, and the upper bound of the ruin probability is minimized.
【學(xué)位授予單位】：重慶理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F840.4;O211.6

【參考文獻】

相關(guān)期刊論文 前2條

1 成世學(xué);破產(chǎn)論研究綜述[J];數(shù)學(xué)進展;2002年05期

2 孔繁亮;B值漸近鞅的估值性質(zhì)[J];應(yīng)用數(shù)學(xué);2004年S2期

本文編號：1974002