本文關(guān)鍵詞： 加權(quán)期望效用 悲觀度 無(wú)穩(wěn)健套利 風(fēng)險(xiǎn)中性概率測(cè)度 參數(shù)二次規(guī)劃　出處：《東華大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：在隨機(jī)區(qū)間收益市場(chǎng)下,風(fēng)險(xiǎn)資產(chǎn)的損益用隨機(jī)區(qū)間表示,可以反映由于信息不完全與投資者主觀認(rèn)識(shí)等因素影響下的資產(chǎn)價(jià)值表現(xiàn)。論文在隨機(jī)區(qū)間市場(chǎng)背景下討論了期望效用優(yōu)化問(wèn)題,概率測(cè)度不確定情形下無(wú)穩(wěn)健套利的穩(wěn)定性以及效用優(yōu)化問(wèn)題。 在隨機(jī)區(qū)間收益市場(chǎng)下,以無(wú)穩(wěn)健套利定價(jià)原則為基礎(chǔ),得到了與經(jīng)典隨機(jī)金融市場(chǎng)類似的風(fēng)險(xiǎn)中性概率測(cè)度。未定權(quán)益的價(jià)格可以由其未來(lái)收益和風(fēng)險(xiǎn)中性概率測(cè)度界定。當(dāng)概率測(cè)度不確定時(shí),產(chǎn)生了無(wú)穩(wěn)健套利性質(zhì)的穩(wěn)定性問(wèn)題。論文基于概率測(cè)度的全變差距離,給出了金融市場(chǎng)模型無(wú)穩(wěn)健套利性質(zhì)不隨概率測(cè)度變化而改變的條件。 論文基于加權(quán)期望效用模型討論了投資者有初始消費(fèi)和未來(lái)不確定財(cái)富情形下的效用優(yōu)化問(wèn)題。研究效用函數(shù)受未來(lái)不確定的隨機(jī)狀態(tài)和隨機(jī)區(qū)間取值狀態(tài)影響下的最優(yōu)效用問(wèn)題。給出了最優(yōu)效用組合存在性的條件。并以最優(yōu)效用組合為基礎(chǔ),構(gòu)建了風(fēng)險(xiǎn)中性概率測(cè)度。同時(shí)也給出了最優(yōu)加權(quán)期望效用的基本性質(zhì)。 論文最后討論了資產(chǎn)未來(lái)?yè)p益的分布不確定情形下的效用優(yōu)化問(wèn)題。在此問(wèn)題中,所獲取的信息僅僅是基本證券未來(lái)?yè)p益表現(xiàn)的一階矩和二階矩,建立了穩(wěn)健加權(quán)期望效用優(yōu)化模型。通過(guò)適當(dāng)方法將穩(wěn)健目標(biāo)轉(zhuǎn)化為雙重標(biāo)準(zhǔn)問(wèn)題,并通過(guò)參數(shù)二次規(guī)劃問(wèn)題加以求解。
[Abstract]:In a stochastic interval income market, the gains and losses of risky assets are expressed in a random interval. It can reflect the performance of asset value under the influence of incomplete information and investors' subjective understanding. This paper discusses the expected utility optimization problem under the background of stochastic interval market. The stability and utility optimization problem of non-robust arbitrage under uncertain probabilistic measures. In the stochastic interval income market, based on the principle of no robust arbitrage pricing, A risk-neutral probability measure similar to the classical stochastic financial market is obtained. The price of contingent equity can be defined by its future income and risk-neutral probability measure. When the probabilistic measure is uncertain, Based on the total variation distance of probabilistic measure, the paper gives the condition that the property of no robust arbitrage in financial market model does not change with the change of probabilistic measure. Based on the weighted expected utility model, this paper discusses the utility optimization problem in the case of investors with initial consumption and uncertain wealth in the future. The utility function is studied by the future uncertain random state and random interval value state shadow. The conditions for the existence of optimal utility combination are given, and based on the optimal utility combination, The risk neutral probability measure is constructed, and the basic properties of optimal weighted expected utility are also given. Finally, the paper discusses the utility optimization problem in the case of uncertain distribution of future gains and losses of assets. In this problem, the information obtained is only the first and second moments of the future profit and loss performance of basic securities. A robust weighted expected utility optimization model is established. The robust objective is transformed into a double standard problem by appropriate methods and solved by the parametric quadratic programming problem.
【學(xué)位授予單位】：東華大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F830.91;F224

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相關(guān)期刊論文 前1條

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本文編號(hào)：1555333