Multiplicative approximation of wealth processes involving no-short-sale strategies via simple trading
Constantinos Kardaras, Eckhard Platen
备注：
11 pages. Revised version. This is the 2nd part of what comprised the older arxiv submission "On financial markets where only buy-and-hold trading is possible" from the two authors
A financial market model with general semimartingale asset-price processes and where agents can only trade using no-short-sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy-and-hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy-and-hold strategies.
Closed-form portfolio optimization under GARCH models
本文首先给出了方差服从Gestival（1，1）过程的现货资产的封闭型最优投资组合配置公式。在Heston and Nandi（2000）Gestern（HN-Gestern）模型下，考虑具有恒定相对风险厌恶（CRRA）效用的投资者希望最大化终端财富的期望效用.得到了最优投资策略、价值函数和最优终端财富的封闭公式。我们发现，最优策略是独立的风险资产的发展，和解决方案的连续时间赫斯顿随机波动率模型收敛，虽然在附加条件。对于每日交易的情况下，最佳的解决方案是相当强大的参数的变化，而数值财富等价损失（WEL）分析表明，良好的性能的赫斯顿解决方案，与一个相当差的性能的默顿解决方案。
Admissible Strategies in Semimartingale Portfolio Selection
在金融市场的数学建模中，选择可接受的交易策略是一个微妙的问题，可以追溯到哈里森和克雷普斯（Harrison and Kreps，1979）。在具有期望效用偏好的最优投资组合选择的背景下，这个问题在过去的二十年里一直是相当关注的焦点。我们提出了一个新的可容许性概念，它具有许多令人愉快的特征：可容许性完全在客观测度下刻画;每个可容许策略可以用有限个交易日的简单策略来近似;任何可容许策略的财富在所有定价测度下都是上鞅;价格过程不需要局部有界;效用函数的严格单调性、严格可微性和可微性都不是必需的;该定义包括经典的均值-方差偏好和单调的期望效用。对于有限的效用函数在整个实数线上，我们的类代表了一个最小的集合，包含简单的策略，也包含优化器，在条件下，比著名的合理渐近弹性条件的效用函数温和。
