【摘要】：風(fēng)險(xiǎn)控制一直是保險(xiǎn)公司的關(guān)鍵問題。在本文中,考慮一個(gè)保險(xiǎn)公司的隨機(jī)控制問題,并且求出保險(xiǎn)公司再保險(xiǎn)和投資的最優(yōu)策略。該保險(xiǎn)公司的盈余過程服從布朗運(yùn)動(dòng)。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(gè)常數(shù),我們對(duì)其模型進(jìn)行拓展,加入兩類狀態(tài)相依的理賠項(xiàng)目,這兩類理賠過程通過一個(gè)共同沖擊聯(lián)系起來。這使得模型更有說服力,并具有實(shí)際意義。通過一些技術(shù)處理,可以將一個(gè)連續(xù)的風(fēng)險(xiǎn)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(xiǎn)公司再保險(xiǎn)的自留份額以及投資風(fēng)險(xiǎn)資產(chǎn)的比例。通過對(duì)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(xiǎn)狀態(tài)相依下的擴(kuò)散逼近模型的驗(yàn)證定理。最后,根據(jù)兩個(gè)具體的實(shí)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(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F840.69

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 楊瀟瀟;梁志彬;張彩斌;;基于時(shí)滯和多維相依風(fēng)險(xiǎn)模型的最優(yōu)期望-方差比例再保險(xiǎn)[J];中國科學(xué):數(shù)學(xué);2017年06期

2 ;Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion[J];Acta Mathematicae Applicatae Sinica;2007年03期

，

本文編號(hào)：2313148