Value Preserving Strategies and a General Framework for Local Approaches to Optimal Portfolios

We present some new general results on the existence and form of value preserving portfolio strategies in a general semimartingale setting. The concept of value preservation is derived via a mean-variance argument. It is also embedded into a framework for local approaches to the problem of portfolio optimization.     

A Martingale Representation Result and an Application to Incomplete Financial Markets

We establish necessary and sufficient conditions for an H¹-martingale to be representable with respect to a collection, of local martingales. M H¹( P ) is representable if and only if M is a local martingale under all p.m.'s Q which are "uniformly equivalent" to P and which make all the elements of local martingales (Theorem 1.1). We then give necessary and sufficient conditions which are easier to verify, and only involve expectations (Theorem 1.2). We go on to apply these results to the problem of pricing claims in an incomplete financial market-establishing two conjectures of Harrison and Pliska(1981).     

Mean-Variance Hedging for Stochastic Volatility Models

In this paper we discuss the tractability of stochastic volatility models for pricing and hedging options with the mean-variance hedging approach. We characterize the variance-optimal measure as the solution of an equation between Doléans exponentials; explicit examples include both models where volatility solves a diffusion equation and models where it follows a jump process. We further discuss the closedness of the space of strategies.     

Consumption and Portfolio Policies With Incomplete Markets and Short-Sale Constraints: the Finite-Dimensional Case1

We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete-time, discrete-state-space securities market with dynamically incomplete markets and short-sale constraints. We characterize the set of feasible consumption bundles as the budget-feasible set defined by constraints formed using the extreme points of the closure of the set of Arrow-Debreu state prices consistent with no arbitrage, and then establish a relationship between the original problem and a dual minimization problem.     

On the Existence of Minimax Martingale Measures

Embedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be an ^d‐semimartingale X and the set of trading strategies consists of all predictable, X‐integrable, ^d‐valued processes H for which the stochastic integral (H.X) is uniformly bounded from below. When the market is free of arbitrage, we show that a sufficient condition for the existence of the minimax measure is that the utility function u : → is concave and nondecreasing. We also show the equivalence between the no free lunch with vanishing risk condition, the existence of a separating measure, and a properly defined notion of viability.     

VAR模型及其在投资组合中的应用

VAR是目前国际上金融风险管理的主流方法之一,本文在对其概念、VAR计算的基本思想和主要特点进行简要介绍、分析的基础上,鉴于VAR已在金融领域中得到了广泛的应用,与投资组合的管理和决策有着密切的联系,重点讨论了基于VAR的投资组合管理,及在VAR约束下的投资组合决策,最后提出了我国在应用VAR所面临的主要问题.     

OPTIMAL PORTFOLIOS WITH LOWER PARTIAL MOMENT CONSTRAINTS AND LPM-RISK-OPTIMAL MARTINGALE MEASURES

We optimize the ratio     over an (arbitrage-free) linear sub-space     of attainable returns in an incomplete market model. If a solution exists for  1 < r < ∞  , then the 1st order optimality condition allows to construct an equivalent martingale measure for     , which is shown to be the solution of an appropriate dual minimization problem over the set of all equivalent martingale measures for     . The dual minimization problem admits a solution iff there exists an equivalent martingale measure for     and its optimal value     equals the lowest upper bound     of all α-ratios over     . This new type of non-concave duality also provides an indifference pricing method. The duality result can be extended to the case     and leads to a new no (approximate) arbitrage condition: "no great expectations with vanishing risk."     

风险态度、金融教育与家庭金融资产选择

文章基于中国城市居民消费金融调查数据,研究了风险态度、金融教育对家庭金融资产选择和家庭金融市场参与的影响。结果发现,风险态度显著影响家庭金融资产组合分散化程度,风险厌恶程度越高,金融资产组合分散化程度越低。风险态度对家庭正规金融市场参与有显著影响,风险厌恶程度的提高会显著降低家庭在股票、基金、债券、储蓄性保险市场的参与概率,风险厌恶程度增加一单位,家庭参与股票市场的可能性会降低10.5%。风险厌恶程度对股票、基金、债券、储蓄性保险资产在家庭金融资产中的比例具有显著的负向影响。家庭的金融教育投入对风险资产持有比重条件分布的影响上,呈先上升后下降趋势,中间分位的要大于两端。文章相应的政策含义是,政府及金融管理部门需要普及金融教育知识,提高居民的金融风险认知水平,从而优化家庭金融资产选择,改善居民金融福利。     

BENCHMARKED RISK MINIMIZATION

This paper discusses the problem of hedging not perfectly replicable contingent claims using the numéraire portfolio. The proposed concept of benchmarked risk minimization leads beyond the classical no‐arbitrage paradigm. It provides in incomplete markets a generalization of the pricing under classical risk minimization, pioneered by Föllmer, Sondermann, and Schweizer. The latter relies on a quadratic criterion, requests square integrability of claims and gains processes, and relies on the existence of an equivalent risk‐neutral probability measure. Benchmarked risk minimization avoids these restrictive assumptions and provides symmetry with respect to all primary securities. It employs the real‐world probability measure and the numéraire portfolio to identify the minimal possible price for a contingent claim. Furthermore, the resulting benchmarked (i.e., numéraire portfolio denominated) profit and loss is only driven by uncertainty that is orthogonal to benchmarked‐traded uncertainty, and forms a local martingale that starts at zero. Consequently, sufficiently different benchmarked profits and losses, when pooled, become asymptotically negligible through diversification. This property makes benchmarked risk minimization the least expensive method for pricing and hedging diversified pools of not fully replicable benchmarked contingent claims. In addition, when hedging it incorporates evolving information about nonhedgeable uncertainty, which is ignored under classical risk minimization.     

基于偏度的多期证券投资组合模型研究

在考虑资产收益率分布中正的偏度水平前提下,以风险价值VaR为约束条件,并引入非线性交易费用、税收等市场摩擦因素,建立以累积偏度最大为目标函数的多期投资组合优化模型,用罚函数法和PSO算法结合求解此模型,并给出实证分析。考虑到在买卖资产风险时交易费用等对投资收益的影响,投资者应该在每一期都对其资产组合进行调整分析,确保在每一期的开始都建立起符合需要的最优资产组合,这对投资者的连续投资行为具有一定的指导意义。     

The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets

Let χ be a family of stochastic processes on a given filtered probability space (Ω, F, (F_t)_t∈T, P) with T?R₊. Under the assumption that the set M_e of equivalent martingale measures for χ is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to P, in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy.     

如何在金融市场中进行资产配置

在金融市场中进行资产配置关键是合理估算资产的相关风险和收益情形,根据投资者状况构建有效的资产配置模型。研究资产配置的基础知识,并就风险度量的方法进行比较分析;考察投资者个人状况,分别针对一般理性投资者和悲观投资者,构建一般资产配置模型和极大极小模型。     

Fundamental Theorems of Asset Pricing for Good Deal Bounds

We prove fundamental theorems of asset pricing for good deal bounds in incomplete markets. These theorems relate arbitrage-freedom and uniqueness of prices for over-the-counter derivatives to existence and uniqueness of a pricing kernel that is consistent with market prices and the acceptance set of good deals. They are proved using duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities.     

Non-convex optimal portfolio sets and constant relative risk aversion

This paper shows by example that, under constant relative risk aversion (CRRA), the set of optimal portfolios can be non-convex even in the presence of a complete set of Arrow-Debreu securities. This implies that, with exclusively CRRA investors, market models without a strong distributional assumption such as that of the capital asset pricing model cannot be tested by testing the optimality of the market portfolio, or by assuming a representative investor. This demonstration extends the key result of Dybvig and Ross [Dybvig, P. H., & Ross S. A. (1982). Portfolio efficient sets. Econometrica, 50, 1525–1546], who showed an example of non-convexity with less restrictive utility assumptions but which could not apply to the case of a complete set of Arrow-Debreu securities.     

基于信用风险修正的多阶段银行贷款组合优化决策模型

针对银行的信用风险和贷款的周期性等问题,建立一个基于信用风险修正的多阶段银行贷款组合优化决策模型,该模型在多阶段模型中考虑了信用风险修正问题,根据模型的特点给出了把Monte Carlo模拟的动态算法和差分进化的多阶段算法相结合的求解方法,前者求解银行各类贷款的期望收益率,后者求解每一阶段银行对各类贷款的最优投资比重。数值试验表明所建立的模型是合理的且符合商业银行的实际操作要求,给出的方法是有效的和可行的。     

A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements

This paper examines optimal consumption and investment choices and the cost of hedging contingent claims in the presence of margin requirements or, more generally, of nonlinear wealth dynamics and constraints on the portfolio policies. Existence of optimal policies is established using martingale and duality techniques under general assumptions on the securities' price process and the investor's preferences. As an illustration, explicit solutions are provided for an agent with ‘logarithmic’ utility. A PDE characterization of the cost of hedging a nonnegative path‐independent European contingent claim is also provided.     

金融市场风险度量方法研究及其实证分析

随着全球金融一体化、自由化进程加速,金融资产市场化、可交易化程度不断加深,金融市场风险逐渐成为金融机构和其他经济主体面对的主要风险之一.基于VaR方法的市场风险测量理论和技术,为测量金融市场风险提供了统一的框架和指标,成为金融市场风险管理的主流方法.在遵循VaR方法的基本框架下,利用VaR进行金融市场风险测量、管理所涉及的基本理论和实证问题进行研究和讨论,结果表明在我国的证券市场上GARCH模型能比较准确的度量市场风险.     

CLOSED-FORM SOLUTIONS FOR OPTIMAL PORTFOLIO SELECTION WITH STOCHASTIC INTEREST RATE AND INVESTMENT CONSTRAINTS

We examine the portfolio choice problem of an investor with constant relative risk aversion in a financial market with partially hedgeable interest rate risk. The individual shadow price of the portfolio constraint is characterized as the solution of a new backward equation involving Malliavin derivatives. A generalization of this equation is studied and solved in explicit form. This result, applied to our financial model, yields closed-form solutions for the shadow price and the optimal portfolio. The effects of parameters such as risk aversion, interest rate volatility, investment horizon, and tightness of the constraint are examined. Applications of our method to a monetary economy with inflation risk and to an international setting with currency risk are also provided.