Worst-case portfolio optimization with proportional transaction costs

We study optimal asset allocation in a crash-threatened financial market with proportional transaction costs. The market is assumed to be either in a normal state, in which the risky asset follows a geometric Brownian motion, or in a crash state, in which the price of the risky asset can suddenly drop by a certain relative amount. We only assume the maximum number and the maximum relative size of the crashes to be given and do not make any assumptions about their distributions. For every investment strategy, we identify the worst-case scenario in the sense that the expected utility of terminal wealth is minimized. The objective is then to determine the investment strategy which yields the highest expected utility in its worst-case scenario. We solve the problem for utility functions with constant relative risk aversion using a stochastic control approach. We characterize the value function as the unique viscosity solution of a second-order nonlinear partial differential equation. The optimal strategies are characterized by time-dependent free boundaries which we compute numerically. The numerical examples suggest that it is not optimal to invest any wealth in the risky asset close to the investment horizon, while a long position in the risky asset is optimal if the remaining investment period is sufficiently large.     

Game options with gradual exercise and cancellation under proportional transaction costs

ABSTRACT

Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomized) stopping time, rather than instantly at an ordinary stopping time. Allowing gradual exercise and cancellation leads to increased flexibility in hedging, and hence tighter bounds on the option price as compared to the case of instantaneous exercise and cancellation. Algorithmic constructions for the bid and ask prices, and the associated superhedging strategies and optimal mixed stopping times for both exercise and cancellation are developed and illustrated. Probabilistic dual representations for bid and ask prices are also established.     

Replication and shortfall risk in a binomial model with transaction costs

The shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs. The author thanks the referee for useful comments on an earlier version of the present paper.     

共同基金和无风险资产投资的最优策略

利用均值-方差模型,分析了非线性交易成本下的共同基金与无风险资产投资组合的有效边界和在一般的效用函数下讨论了投资者的最优投资策略.     

排污权交易成本动因分析

排污权交易制度作为控制污染超量排放的方法之一,其有效实施必须以降低市场交易成本为前提.从国内外交易成本理论出发,分别从外部环境和企业内部分析排污权交易成本的形成机理和影响因素,提出降低排污权交易成本、提高交易效率的方法,为构建排污权交易市场提供理论指导和支持.     

证券投资组合优化问题的强健性的锥优化方法(英文)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

Optimization of component reliability in the design phase of capital goods

We introduce a quantitative model to support the decision on the reliability level of a critical component during its design. We consider an OEM who is responsible for the availability of its systems in the field through service contracts. Upon a failure of a critical part in a system during the exploitation phase, the failed part is replaced by a ready-for-use part from a spare parts inventory. In an out-of-stock situation, a costly emergency procedure is applied. The reliability levels and spare parts inventory levels of the critical components are the two main factors that determine the downtime and corresponding costs of the systems. These two levels are decision variables in our model. We formulate the portions of Life Cycle Costs (LCC) which are affected by a component’s reliability and its spare parts inventory level. These costs consist of design costs, production costs, and maintenance and downtime costs in the exploitation phase. We conduct exact analysis and provide an efficient optimization algorithm. We provide managerial insights through a numerical experiment which is based on real-life data.     

关于高校学分制教材管理的思考

教材管理是高校教学管理工作的重要环节。而高校学分制的实行对教材管理提出了更新的、更高的要求，传统的教材管理势必为新的管理模式所取代，这是一个趋势，也是一个发展方向。在学分制下，教材管理应是符合后现代教育思想理念的，由规定、强制的管理方式转向组织、服务的管理方式，在学生与教材科之间建立一个信息共享、资源共享的教材管理系统，树立教材管理是公共服务的全新理念，提高学校教材管理部门的公共管理意识，提高管理者自身的公共管理能力。     

Portfolio selection with transaction costs under expected shortfall constraints

An investor subject to proportional transaction costs allocates funds to multiple stocks and a bank account, to maximise the expected growth rate of the portfolio value under Expected Shortfall (ES) constraints. In a numerical example with ten time steps and one stock important innovations are caused by the introduction of the Expected Shortfall constraint: First, expected returns are reduced by less than one-tenth when the ES constraint is introduced. In comparison, economic capital as measured by ES, is reduced to amounts between one-half and three-quarters, when the ES constraint is introduced. Second, the dependence of expected return and ES on the initial portfolio, in particular when transaction costs are high, is largely removed by the introduction of the ES constraint.     

指令驱动市场的流动性成本及影响因素分析

结合价格和申报数量，构建了指令驱动市场中股票流动性成本的事前测度方法，并采用上海证券市场的股票实时行情数据分析了流动性成本及影响因素．结论表明：上海股市的相对流动性成本呈“L”形曲线；随着股票价格、平均交易规模、波动性和非流通股所占总股本比例的增加，相对流动性成本逐渐增加；随着换手率的增加，相对流动性成本逐渐减少．