【摘要】：風(fēng)險控制一直是保險公司的關(guān)鍵問題。在本文中,考慮一個保險公司的隨機(jī)控制問題,并且求出保險公司再保險和投資的最優(yōu)策略。該保險公司的盈余過程服從布朗運(yùn)動。受到Browne (1995)工作的啟發(fā),該文章中理賠是連續(xù)的且是一個常數(shù),我們對其模型進(jìn)行拓展,加入兩類狀態(tài)相依的理賠項目,這兩類理賠過程通過一個共同沖擊聯(lián)系起來。這使得模型更有說服力,并具有實際意義。通過一些技術(shù)處理,可以將一個連續(xù)的風(fēng)險過程看作復(fù)合泊松模型的擴(kuò)散逼近。在這一過程下,可以推導(dǎo)出模型到達(dá)預(yù)設(shè)上界的概率,并且能夠得到值函數(shù)以及最優(yōu)策略,包括保險公司再保險的自留份額以及投資風(fēng)險資產(chǎn)的比例。通過對比之前的結(jié)論,發(fā)現(xiàn)最優(yōu)策略不僅僅依賴于利率和盈余,而且還依賴于安全負(fù)荷�；陔S機(jī)控制的理論,我們首先證明了擴(kuò)散逼近模型的一些性質(zhì),之后提出了風(fēng)險狀態(tài)相依下的擴(kuò)散逼近模型的驗證定理。最后,根據(jù)兩個具體的實例,求出具體的策略以及值函數(shù)。
[Abstract]:Risk control has always been a key issue for insurance companies. In this paper, we consider a stochastic control problem of an insurance company, and find out the optimal strategy of reinsurance and investment of insurance company. The insurance company's earnings process services from the Brownian motion. Inspired by the work of Browne (1995), claims in this paper are continuous and a constant. We extend the model and add two kinds of state-dependent claim items, which are connected by a common impact. This makes the model more convincing and has practical significance. Through some technical treatment, a continuous risk process can be regarded as the diffusion approximation of the compound Poisson model. In this process, the probability of the model reaching the preset upper bound can be derived, and the value function and the optimal strategy can be obtained, including the retention share of the reinsurance company and the proportion of the investment risk assets. By comparing the previous conclusions, we find that the optimal strategy depends not only on interest rate and earnings, but also on safety load. Based on the theory of stochastic control, we first prove some properties of diffusion approximation model, and then propose a verification theorem for diffusion approximation model with dependent risk state. Finally, according to two concrete examples, the concrete strategy and value function are obtained.
【學(xué)位授予單位】：南京師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F840.69

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相關(guān)期刊論文 前2條

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本文編號：2313148