本文選題：隨機(jī)最優(yōu)控制　切入點(diǎn)：再保險(xiǎn)　出處：《暨南大學(xué)》2013年碩士論文

【摘要】：隨著保險(xiǎn)行業(yè)的蓬勃發(fā)展，保險(xiǎn)規(guī)模逐漸擴(kuò)大，保險(xiǎn)公司面臨的風(fēng)險(xiǎn)也不斷增大。為了分散風(fēng)險(xiǎn)，，穩(wěn)定經(jīng)營(yíng)，保險(xiǎn)公司需要采取再保險(xiǎn)的措施來將自身部分風(fēng)險(xiǎn)轉(zhuǎn)移出去。而在減少風(fēng)險(xiǎn)同時(shí)必然伴隨著保費(fèi)的分?jǐn)�，�?duì)保險(xiǎn)公司而言意味著可盈利的資本減少，所以保險(xiǎn)公司需要在再保險(xiǎn)的收益與風(fēng)險(xiǎn)兩者關(guān)系中達(dá)到平衡。同時(shí)保險(xiǎn)公司為追求盈利可以將積累的保費(fèi)投資于金融市場(chǎng)獲取預(yù)期收益。投資帶來風(fēng)險(xiǎn)，將必然面臨投資收益與風(fēng)險(xiǎn)的抉擇問題。因此，探索最優(yōu)再保險(xiǎn)和投資策略對(duì)保險(xiǎn)公司的發(fā)展而言至關(guān)重要。 本文主要運(yùn)用隨機(jī)最優(yōu)控制理論，通過建立動(dòng)態(tài)規(guī)劃模型來解決最優(yōu)再保險(xiǎn)和投資問題。首先在擴(kuò)散風(fēng)險(xiǎn)模型中引入再保險(xiǎn)。當(dāng)保險(xiǎn)公司將盈余投資到常數(shù)彈性變差（CEV）模型描述的風(fēng)險(xiǎn)資產(chǎn)和無風(fēng)險(xiǎn)資產(chǎn)時(shí)，應(yīng)用動(dòng)態(tài)規(guī)劃原理以期望效用最大化為目標(biāo)取得值函數(shù)滿足的HJB方程。然后利用Legendre變化-對(duì)偶方法在不同效用函數(shù)準(zhǔn)則下，得到最優(yōu)再保險(xiǎn)和投資策略。最后結(jié)合數(shù)值圖像分析各個(gè)相關(guān)參數(shù)與最優(yōu)再保險(xiǎn)投資策略之間的聯(lián)系。
[Abstract]:With the booming development of the insurance industry, the scale of insurance is gradually expanding, and the risks faced by insurance companies are also increasing. Insurance companies need to take reinsurance measures to transfer part of their own risk. And reducing risk must be accompanied by premium allocation, which means less profitable capital for insurance companies. So insurance companies need to strike a balance between reinsurance returns and risks. And insurance companies can invest their accumulated premiums in the financial markets for profit. Investment brings risks. Therefore, it is very important to explore the optimal reinsurance and investment strategy for the development of insurance companies. In this paper, the stochastic optimal control theory is mainly used. The optimal reinsurance and investment problems are solved by establishing a dynamic programming model. Firstly, reinsurance is introduced into the diffusion risk model. When the insurance company invests surplus in the risk assets and risk-free assets described by the constant elasticity variation (CEV) model, Using the principle of dynamic programming to obtain the HJB equation satisfying the value function with the goal of maximizing expected utility, then using the Legendre variable-duality method under different utility function criteria. The optimal reinsurance and investment strategy are obtained. Finally, the relationship between the relevant parameters and the optimal reinsurance investment strategy is analyzed with numerical images.
【學(xué)位授予單位】：暨南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F840.4;F224;O212.1

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