【摘要】：研究不完備市場中最大化期望消費效用準(zhǔn)則下的最優(yōu)消費/投資決策及期權(quán)定價問題.在標(biāo)的資產(chǎn)價格服從幾何均值回復(fù)變化的假設(shè)下,利用隨機動態(tài)規(guī)劃理論及消費效用無差別定價原理得到了最優(yōu)消費/投資策略以及標(biāo)的資產(chǎn)不可交易的歐式期權(quán)價格所滿足的偏微分方程.給出了數(shù)值算例,結(jié)果表明投資者的風(fēng)險厭惡態(tài)度會降低期權(quán)的效用價格,而標(biāo)的資產(chǎn)的均值回復(fù)特性使得期權(quán)價格隨時間的變化規(guī)律受控于標(biāo)的資產(chǎn)均衡價格水平,分情況可表現(xiàn)出單調(diào)遞增和單調(diào)遞減的2種不同變化趨勢.
[Abstract]:This paper deals with the optimal consumption / investment decision and option pricing under the criterion of maximizing expected consumption utility in incomplete markets. On the assumption that the underlying asset price changes back from the geometric mean, By using stochastic dynamic programming theory and the principle of non-differential pricing of consumption utility, the partial differential equations of optimal consumption / investment strategy and non-tradable European option price of underlying assets are obtained. A numerical example is given. The results show that the investor's risk-aversion attitude will reduce the utility price of the option, while the average return property of the underlying asset makes the variation of the option price with time controlled by the equilibrium price level of the underlying asset. There are two different trends of monotone increasing and monotone decreasing.
【作者單位】： 湖南大學(xué)金融與統(tǒng)計學(xué)院;南京審計學(xué)院數(shù)學(xué)與統(tǒng)計學(xué)院;南京審計學(xué)院金融學(xué)院;
【基金】：國家自然科學(xué)基金資助項目(70971037) 江蘇省高校青藍(lán)工程項目 南京審計學(xué)院青年課題資助項目(NSK2009/C06)
【分類號】：F830.9;F224

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