本文關(guān)鍵詞： 不完備市場(chǎng) 最優(yōu)投資 效用無差別定價(jià) HJB方程　出處：《西南財(cái)經(jīng)大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：投資組合選擇和金融資產(chǎn)定價(jià)問題一直是現(xiàn)代金融理論研究的核心內(nèi)容。關(guān)于動(dòng)態(tài)投資組合的研究主要是在Merton模型的基礎(chǔ)上進(jìn)行改進(jìn),探討不同投資環(huán)境下風(fēng)險(xiǎn)厭惡投資者的最優(yōu)選擇。關(guān)于完備市場(chǎng)金融資產(chǎn)定價(jià)的研究主要是基于無套利理論,但是當(dāng)市場(chǎng)不完備時(shí),由于存在多個(gè)等價(jià)鞅測(cè)度而無法得到資產(chǎn)的唯一價(jià)格。HodgesNeuberger提出的效用無差別定價(jià)理論為解決不完備市場(chǎng)中金融資產(chǎn)定價(jià)問題提供了理論基礎(chǔ)。因此,本文基于隨機(jī)控制理論研究以下兩個(gè)問題： (1)具有線性消費(fèi)模式的最優(yōu)投資。當(dāng)投資者具有線性消費(fèi)時(shí),就有可能發(fā)生破產(chǎn),而傳統(tǒng)的Merton問題并沒有考慮破產(chǎn)的可能性。本文利用隨機(jī)控制理論得到了投資者的最優(yōu)投資策略以及價(jià)值函數(shù)滿足的偏微分方程,然后分別在指數(shù)效用和冪效用函數(shù)下得到了投資者的最優(yōu)投資策略的顯示解。 (2)不完備市場(chǎng)中風(fēng)險(xiǎn)資產(chǎn)的效用無差別定價(jià)。在不完備市場(chǎng)中,首先假設(shè)利率是常數(shù)時(shí),根據(jù)效用無差別定價(jià)理論得到了風(fēng)險(xiǎn)資產(chǎn)的效用無差別價(jià)格滿足的偏微分方程,并且在指數(shù)效用函數(shù)下得到了效用無差別價(jià)格的顯示解。其次假設(shè)市場(chǎng)具有Ho-Lee利率模型,重新得到了不完備市場(chǎng)中風(fēng)險(xiǎn)資產(chǎn)的效用無差別價(jià)格滿足的偏微分方程。
[Abstract]:Portfolio selection and financial asset pricing have always been the core contents of modern financial theory. The research on dynamic portfolio is mainly based on Merton model. This paper discusses the optimal choice of risk-averse investors in different investment environments. The research on the pricing of financial assets in the complete market is mainly based on the theory of no arbitrage, but when the market is not complete, Due to the existence of multiple equivalent martingale measures, it is impossible to obtain the unique price of assets. HodgesNeuberger's Utility Non-differential pricing Theory provides a theoretical basis for solving the pricing problem of financial assets in incomplete markets. In this paper, based on stochastic control theory, the following two problems are studied:. An optimal investment with a linear consumption pattern. When an investor has a linear consumption, it is possible to go bankrupt. However, the traditional Merton problem does not consider the possibility of bankruptcy. In this paper, the optimal investment strategy of investors and the partial differential equation satisfying the value function are obtained by using stochastic control theory. Then under the exponential utility function and the power utility function, the display solution of investors' optimal investment strategy is obtained. In incomplete market, when the interest rate is constant, the partial differential equation of utility nondifferential price is obtained according to the theory of utility nondifferential pricing. Moreover, under the exponential utility function, we obtain the explicit solution of the utility undifferentiated price. Secondly, assuming that the market has the Ho-Lee interest rate model, we obtain the partial differential equation of the utility of the risk asset in the incomplete market.
【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F830.91

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本文編號(hào)：1553107