本文選題：Bessel過程　切入點：最優(yōu)交易策略　出處：《華南理工大學》2014年碩士論文

【摘要】：經(jīng)典的無套利理論中因為不存在套利機會，未定權(quán)益都可以實現(xiàn)完全對沖，而在不完備市場中存在套利機會，未定權(quán)益不能實現(xiàn)完全對沖，一個給定的未定權(quán)益可以有不同的方法或途徑實現(xiàn)某種意義上的最優(yōu)對沖，本文以初始資金最小并達到給定最終收益的策略作為最優(yōu)對沖策略。本文主要研究資產(chǎn)價格模型為借助Bessel過程定義的連續(xù)時間馬爾可夫過程情形下的最優(yōu)對沖策略。 首先，定義了不完備市場中資產(chǎn)價格的一般模型及交易策略，引入推廣夏普比率為多維形式的市場風險價格(MPR)，且在市場風險價格的基礎(chǔ)上定義了貼現(xiàn)因子(SDF)，用馬爾可夫MPR定義的貼現(xiàn)因子構(gòu)造對沖價格函數(shù)h p。其次，推導出對沖價格函數(shù)的伊藤過程表示，并化簡為財富過程形式，，該策略即為最優(yōu)對沖策略，同時根據(jù)相應(yīng)的假設(shè)和相關(guān)理論獲得了對沖價格函數(shù)的光滑性。最后，從已存在的測度變換推導出的廣義的測度變換，簡化了資產(chǎn)價格模型和隨機貼現(xiàn)因子(SDF)的倒數(shù)的動態(tài)特性，從而使對沖價格函數(shù)和最優(yōu)對沖策略的計算更加簡便。 本文最后分別對以不帶漂移項和帶漂移項的n維Bessel過程為輔助過程定義的資產(chǎn)價格模型得到了具體的最優(yōu)對沖策略。通過前面所證的結(jié)果，以馬爾可夫貼現(xiàn)因子構(gòu)造對沖價格函數(shù)，化簡為財富過程形式得到最優(yōu)策略，并通過和已存在的例子進行對比，證實該策略即為最優(yōu)對沖策略。
[Abstract]:In the classical no-arbitrage theory, because there is no arbitrage opportunity, the contingent equity can be completely hedged, but in the incomplete market there is arbitrage opportunity, and the contingent equity can not be fully hedged. A given contingent claim can have different ways or means of achieving an optimal hedge in a sense, In this paper, the minimum initial capital and the given final return are taken as the optimal hedging strategies. In this paper, the asset price model is the optimal hedging strategy under the continuous time Markov process defined by the Bessel process. Firstly, the general model and trading strategy of asset price in incomplete market are defined. This paper introduces the market risk price which generalizes Sharpe ratio to multidimensional form, and defines the discount factor based on the market risk price. The discount factor defined by Markov MPR is used to construct the hedge price function h p. The Ito process representation of the hedge price function is derived and simplified to the wealth process form. The strategy is the optimal hedging strategy, and the smoothness of the hedge price function is obtained according to the corresponding assumptions and relevant theories. The generalized measure transformation derived from the existing measure transformation simplifies the dynamic properties of the reciprocal of asset price model and stochastic discount factor (SDF), thus making the calculation of hedge price function and optimal hedging strategy easier. In the end of this paper, the optimal hedging strategies are obtained for the asset price models defined by the n-dimensional Bessel processes with and without drift terms, respectively. The hedging price function is constructed by Markov discount factor, and the optimal strategy is obtained in the form of wealth process. By comparing with the existing examples, it is proved that this strategy is the optimal hedging strategy.
【學位授予單位】：華南理工大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F224;F830.91

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