带交易费用的证券组合投资选择的优化模型

本文利用在约束条件中加入证券多样化选择约束的办法来抵减非系统风险 ,就证券组合投资的选择问题 ,建立了带交易费用的综合考虑收益和风险的多目标规划模型 ,然后通过变换将不可微的多目标规划问题转化为一个多目标线性规划问题 ,最后给出了问题的一个算法和算例     

Designing and pricing guarantee options in defined contribution pension plans

The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. However, for DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio and we develop a discrete model that selects the reference portfolio to minimize the cost of a guarantee. While the relation DB–DC is typically viewed as a binary one, the model shows how to price a wide range of guarantees creating a continuum between DB and DC. Integrating guarantee pricing with asset allocation decision is useful to both pension fund managers and regulators. The former are given a yardstick to assess if a given asset portfolio is fit-for-purpose; the latter can assess differences of specific reference funds with respect to the optimal one, signaling possible cases of moral hazard. We develop the model and report numerical results to illustrate its uses.     

不同风险度量方法的投资组合比较研究

为了验证投资组合理论在中国证券市场的有效性,在不允许卖空情况,针对不同风险度量方法,文章运用旋转算法或结合序列二次规划法分别求解均值-方差、均值-下半方差投资组合模型、均值-半绝对偏差、均值-平均绝对偏差和均值-VaR.文章选取三年沪市六只业绩比较好的股票,依据前两年的数据作为样本数据,分别求出五个模型在不同期望收益率下的最优投资策略,将得出的最优投资策略应用到最后一年,进行模拟投资,从而计算出各模型的总收益率.以等比例投资为标准,比较五个模型的绩效.最后,证明了两个模型对于中国证券市场是适用.     

极大极小投资组合选择模型和均衡价格系统

讨论了市场上不存在无风险资产条件下投资组合选择的极大极小模型,推导出市场上不存在无风险资产时极大极小模型的最优投资策略和有效前沿,得到了资本市场均衡时存在唯一的非负均衡价格系统的充分必要条件和各资产均衡价格的解析表达式.     

Lose oneself in comparison: An investment and consumption game between two agents

We study an investment and consumption model with two agents. Each agent may derive extra utilities (disutilities) from positive (negative) outcomes of comparisons between her and the other agent’s consumption levels. In the unique Nash equilibrium, comparison induces the more (less) risk averse agent to invest more aggressively (conservatively) and the more (less) patient agent to increase consumption earlier (later). Adopting these distorted policies can be costly when agents’ real welfare is measured by their absolute consumption levels.     

Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints

This paper studies the risk management in a defined contribution (DC)pension plan. The financial market consists of cash, bond and stock. The interest rate in our model is assumed to follow an Ornstein–Uhlenbeck process while the contribution rate follows a geometric Brownian Motion. Thus, the pension manager has to hedge the risks of interest rate, stock and contribution rate. Different from most works in DC pension plan, the pension manger has to obtain the optimal allocations under loss aversion and Value-at-Risk(VaR) constraints. The loss aversion pension manager is sensitive to losses while the VaR pension manager has to ensure the quality of wealth at retirement. Since these problems are not standard concave optimization problems, martingale method is applied to derive the optimal investment strategies. Explicit solutions are obtained under these two optimization criterions. Moreover, sensitivity analysis is presented in the end to show the economic behaviors under these two criterions.     

Insurability of catastrophic risks: the stochastic optimization model

Catastrophes produce losses highly correlated in space and time, which break the law of large numbers. We derive the insurability of dependent catastrophic risks by calculating conditions that would aid insurers in deliberate selection of their portfolios. This paper outlines the general structure of a basic stochastic optimization model. Connections between the probability of ruin and nonsmooth risk functions, as well as adaptive Monte Carlo optimization procedures and path dependent laws of large numbers, are discussed     

Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs

Abstract

Portfolio theory covers different approaches to the construction of a portfolio offering maximum expected returns for a given level of risk tolerance where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this article, a risk averse power utility function is studied in discrete time for a large class of underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximizes the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods when the proportional transaction costs are small and by using expansions about critical points for large transaction costs.     

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.     

Portfolio optimization via stochastic programming: Methods of output analysis

Solutions of portfolio optimization problems are often influenced by errors or misspecifications due to approximation, estimation and incomplete information. Selected methods for analysis of results obtained by solving stochastic programs are presented and their scope illustrated on generic examples – the Markowitz model, a multiperiod bond portfolio management problem and a general strategic investment problem. The approaches are based on asymptotic and robust statistics, on the moment problem and on results of parametric optimization.