【摘要】：研究了具有兩個(gè)業(yè)務(wù)部門的保險(xiǎn)公司的最優(yōu)投資問(wèn)題,其中每個(gè)業(yè)務(wù)部門的盈余過(guò)程由二維的Lévy過(guò)程描述。保險(xiǎn)公司可將其盈余投資于金融市場(chǎng),其中金融市場(chǎng)由一個(gè)無(wú)風(fēng)險(xiǎn)資產(chǎn)和兩個(gè)具有風(fēng)險(xiǎn)相關(guān)性的風(fēng)險(xiǎn)資產(chǎn)組成,而且風(fēng)險(xiǎn)資產(chǎn)的價(jià)格過(guò)程由二維的Lévy過(guò)程所驅(qū)動(dòng)。文中討論了兩個(gè)優(yōu)化問(wèn)題。一個(gè)是基準(zhǔn)問(wèn)題,即選擇適當(dāng)?shù)耐顿Y策略使保險(xiǎn)公司的終端財(cái)富與一個(gè)基準(zhǔn)值之差的平方期望最小;另一個(gè)是均值-方差(M-V)問(wèn)題,即在保險(xiǎn)公司終端財(cái)富給定的情形下,選擇適當(dāng)?shù)耐顿Y策略使終端財(cái)富的方差最小。利用動(dòng)態(tài)規(guī)劃的方法,得到第一個(gè)優(yōu)化問(wèn)題的最優(yōu)投資策略和最優(yōu)值函數(shù)的解析式。結(jié)合第一個(gè)優(yōu)化問(wèn)題的結(jié)果,利用對(duì)偶定理得到第二個(gè)優(yōu)化問(wèn)題的最優(yōu)投資策略和有效前沿。
[Abstract]:The optimal investment problem of insurance companies with two business units is studied, in which the earnings process of each business sector is described by a two-dimensional L 茅 vy process. Insurance companies can invest their earnings in financial markets, in which the financial market consists of a risk-free asset and two riskless risk assets, and the price process of the risky assets is driven by the two-dimensional L 茅 vy process. Two optimization problems are discussed in this paper. One is the benchmark problem, that is, choosing the appropriate investment strategy to minimize the square expectation of the difference between the terminal wealth of the insurance company and a benchmark value; the other is the mean-variance (M-V) problem, that is, when the insurance company's terminal wealth is given, Choose the appropriate investment strategy to minimize the variance of terminal wealth. The optimal investment strategy and optimal value function of the first optimization problem are obtained by using the dynamic programming method. Combined with the results of the first optimization problem, the optimal investment strategy and efficient frontier of the second optimization problem are obtained by using the duality theorem.
【作者單位】： 中山大學(xué)數(shù)學(xué)與計(jì)算科學(xué)學(xué)院;廣東工業(yè)大學(xué)應(yīng)用數(shù)學(xué)學(xué)院;中山大學(xué)金融工程與風(fēng)險(xiǎn)管理研究中心;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(71201173,71231008) 珠江學(xué)者支持計(jì)劃資助項(xiàng)目 廣東省高層次人才資助項(xiàng)目
【分類號(hào)】：F842.3;O212.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 張明善;姚s，

本文編號(hào)：2176662