本文選題：時(shí)間一致　切入點(diǎn)：均值方差　出處：《中南大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：本文主要研究不同金融市場(chǎng)下,具有不同風(fēng)險(xiǎn)厭惡系數(shù)的兩個(gè)投資者在不同風(fēng)險(xiǎn)模型下的投資組合博弈問(wèn)題。 首先研究在一個(gè)簡(jiǎn)單金融市場(chǎng)下兩個(gè)投資者之間的投資組合選擇問(wèn)題。假設(shè)金融市場(chǎng)由一個(gè)無(wú)風(fēng)險(xiǎn)資產(chǎn)和兩個(gè)相關(guān)的風(fēng)險(xiǎn)資產(chǎn)構(gòu)成,分別考慮兩個(gè)投資者在風(fēng)險(xiǎn)資產(chǎn)價(jià)格服從幾何布朗運(yùn)動(dòng)模型以及Heston隨機(jī)方差模型時(shí)的時(shí)間一致均值-方差投資組合選擇問(wèn)題。利用動(dòng)態(tài)規(guī)劃原理(推廣的Hamilton-Jacobi-Bellman (HJB)方程),給出相應(yīng)的檢驗(yàn)定理,分別得到不同模型下兩個(gè)投資者的最優(yōu)投資策略和最優(yōu)值函數(shù)的顯式解。然后研究由兩個(gè)保險(xiǎn)公司組成的簡(jiǎn)單市場(chǎng)情形下,只投資于一個(gè)無(wú)風(fēng)險(xiǎn)資產(chǎn)時(shí)的時(shí)間一致均值-方差比例再保險(xiǎn)博弈問(wèn)題。此時(shí)保險(xiǎn)公司為分散風(fēng)險(xiǎn)進(jìn)行比例再保險(xiǎn)安排。通過(guò)求解相應(yīng)的推廣的HJB方程,得到保險(xiǎn)公司的最優(yōu)比例再保險(xiǎn)策略和最優(yōu)值函數(shù)的顯式表達(dá)式。通過(guò)相關(guān)數(shù)值計(jì)算得到最優(yōu)策略與模型主要參數(shù)之間的關(guān)系及當(dāng)一些參數(shù)變化時(shí)的最優(yōu)策略變化趨勢(shì),給出相應(yīng)的分析。
[Abstract]:This paper focuses on the portfolio game problem of two investors with different risk aversion coefficients under different risk models in different financial markets. This paper first studies the problem of portfolio selection between two investors in a simple financial market. Suppose the financial market consists of a risk-free asset and two associated risky assets. The time-consistent mean-variance portfolio selection problem of two investors in the geometric Brownian Motion Model and the Heston Stochastic Variance Model of Venture Asset Price is considered respectively. The dynamic programming principle (extended Hamilton-Jacobi-Bellman / HJB) is used to solve the problem. Cheng, the corresponding test theorem is given. The explicit solutions of the optimal investment strategy and optimal value function of two investors under different models are obtained respectively. When only one risk-free asset is invested, the time consistent mean-variance proportional reinsurance game problem is solved. In this case, the insurance company carries out proportional reinsurance arrangements for decentralized risk. By solving the corresponding generalized HJB equation, The explicit expressions of the optimal proportional reinsurance strategy and the optimal value function of the insurance company are obtained. The relationship between the optimal strategy and the main parameters of the model and the change trend of the optimal strategy when some parameters change are obtained by the correlation numerical calculation. The corresponding analysis is given.
【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F830.9

【共引文獻(xiàn)】

相關(guān)期刊論文 前3條

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本文編號(hào)：1581563