基于效用的无界随机禀赋最优投资 定价

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摘要翻译：
本文研究了具有无界随机禀赋且效用函数同时支持正负财富的金融主体的最终财富期望效用最大化问题。我们证明了一类允许策略--财富过程为上鞅的策略--在所有相对熵有限的定价测度下，最优交易策略的存在性。给出了基于效用的套利不存在的充要条件，以及原始问题存在解的充要条件。我们考虑了两种基于效用的方法，可以用来对未定权益进行定价。首先，我们研究了基于边际效用的价格过程(MUBPP's)。我们证明了在效用最大化投资者的归一化最优对偶测度下，这类过程可以刻画为局部鞅。最后，我们给出了效用无差异价格的一些新结果，包括一般效用函数、无界禀赋和无界未定权益情形的连续性和体积渐近性。
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英文标题：
《Optimal Investment with an Unbounded Random Endowment and Utility-Based
  Pricing》
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作者：
Mark Owen, Gordan Zitkovic
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最新提交年份：
2007
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

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英文摘要：
  This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -- those strategies whose wealth process is a supermartingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem.   We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.
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PDF链接：
https://arxiv.org/pdf/0706.0478

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关键词：Optimization Applications Indifference Differential Quantitative based 定价 效用 禀赋 problem