EXISTENCE OF STOCHASTIC EQUILIBRIUM WITH INCOMPLETE FINANCIAL MARKETS

This paper analyzes the aritrage-tree security markets and the general equilibrium ex-istence problem for a stochastic economy with incomplete financial markets. Information structure is given by an event tree. This paper restricts attention to puraly financial securities. It isassume that trading takes place in the sequence of spot markets and futures markets for securi-ties payable in units of account. Unlimited short-selling in securities is allowed. Financial markets may be incomplete, some consumption streams may be impossible to obtain by any tradingstrategy. Securities may be individually precluded from trade at arbitrary states and dates. Thesecurity price process is arbitrage-free the dividend process if and only if there exists a stochaticstate price (present value) process : the present value of the security prices at every vertex isthe present value of their dividend and capital values over the set of immediate successors ; thecurrent value of each security at every vertex is the present value of its future dividend streamover all succeeding vertices. The existence of such an equilibrium is proved under the followingcondition: continuous, weakly convex, strictly monotone and complete preferences, strictlypositive endowmenta and dividends processes.     

The effect of market power on risk-sharing

The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent’s set of strategic choices consists of the security payoffs and the pricing kernel that are consistent with the optimal-sharing rules; while in the incomplete setting, agents respond via demand functions on a vector of given tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium, the sharing securities are suboptimal, since agents submit for sharing different risk exposures than their true endowments. On the other hand, the Nash equilibrium prices stay unaffected by the game only in the special case of agents with the same risk aversion. In addition, agents with sufficiently lower risk aversion act as predatory traders, since they absorb utility surplus from the high risk averse agents and reduce the efficiency of sharing. The main results of the paper also hold under the generalized models that allow the presence of noise traders and heterogeneity in agents’ beliefs.     

Asset Pricing under Progressive Taxes and Existence of General Equilibrium

This paper shows that the existence of general equilibrium in a two-period economy with financial markets and progressive anonymous tax system is not at all problematic, provided securities are purely financial. We explore the concepts of weakly and strongly arbitrage-free security price for return and tax system, and prove arbitrage-free asset pricing theorems without short-sale restrictions. A general equilibrium is a set of current and future prices (contingent on uncertain events) and a set of individual plans such that all markets are cleared. The existence of such an equilibrium is proved under the following conditions: continuous, weakly convex, strictly monotone, complete preferences and strictly positive endowments.     

The challenge in managing new financial risks: adopting an heuristic or theoretical approach

The financial crisis began with the collapse of Lehman Brothers and the subprime asset backed securities debacle. Credit risk was turned into liquidity risk, resulting in a lack of confidence among financial institutions. In this article, we will propose a way to model liquidity risk and the credit risk in best practices. We will show that liquidity risk is a new type of risk and the current way to deal with it is based solely on observed variables without any theoretical link. We propose an heuristic approach to combine the numerous liquidity risk indicators with a logistic regression for the first time. In regards to credit risk, several articles prove that the best practice is to use an option model to appreciate this risk. We will present our methodology using stochastic diffusion for the interest rate because currently the yield curves aren’t liquid. This approach is more relevant because the basis model in prior publications has a constant interest rate or a forward rate. Both models allow a better understanding of liquidity and credit risks and the further development of research deals with the link between these two financial risks.     

证券数目变化时受到扰动的M-V有效前沿分析

基于M-V证券组合模型,在证券市场上不存在无风险资产且允许卖空条件下,探讨了证券数增加k种后原n种证券协方差矩阵发生改变情形下M-V证券组合有效前沿的漂移问题。通过引入扰动因子和扰动矩阵,给出了M-V证券组合有效前沿的漂移方向及其开口大小的变化情况．研究结果表明证券数增加了k种后有效前沿向左漂移以及它的开口变大,原证券组合的有效前沿完全落在新的证券组合可行集内．     

Simulation modelling and analysis of a border security system

Border control is vital to the security of a nation and its citizens. All countries look at measures to improve the security of their borders. But increasing security can bring a substantial financial burden. In this study, we analyze the border security problem of Turkey using a simulation approach. Our main objective is to find more efficient ways of improving border control and security along Turkey’s land borders. To achieve this, we examine the structure of the border security system and its major elements, examine the relationships between performance measures, and assess the effectiveness of security elements on each system performance measure. We also look into the issues of planned changes and additional resources, and we evaluate new alternative system designs. The results of simulation experiments are analyzed by statistical methods.     

Multivariate geometric stable distributions in financial applications

We describe a class of multivariate geometric stable laws that can be used in modeling multivariate financial portfolios of securities. These heavy tailed distributions are stable with respect to geometric summation and accommodate the possibility of market crashes. We look at bivariate currency exchange rates data and show that its main features, peakedness and heavy tails, are very well captured by the geometric stable model.     

A note on constant proportion trading strategies

We consider constant proportion (CP) trading strategies when there are multiple underlying securities and use a recently derived expression for the terminal wealth of a CP strategy to address two issues. First, we characterize the performance of a CP strategy relative to the performance of the corresponding buy-and-hold strategy. We then explain the performance of leveraged ETFs which have been criticized for not performing as expected, particularly during the financial crisis of 2008.     

突发公共卫生事件对系统性金融风险的冲击及传染效应研究

首先基于面板向量自回归模型考察了突发公共卫生事件对系统性金融风险的冲击影响,接着综合考虑突发公共卫生事件的影响及其所导致的收益率的非对称性构建单指标非对称CoVaR模型,最后借助LASSO惩罚函数与局部估计法进行求解,以此构建有向网络分析金融机构间的传染效应.研究发现:(1)突发公共卫生事件冲击会使系统性金融风险水平短...     

不完全金融市场货币平衡存在性(英)

本文研究不完全金融市场中具有货币政策的货币经济一般平衡存在性．我们只考虑纯金融市场，允许卖空，金融市场是不完全的；一些商品流不可能由交易策略得到．具有连续、弱凸性、严格单调和完全偏好，严格正初始占有和红利过程的经济则存在货币平衡．     

Optimal life-insurance selection and purchase within a market of several life-insurance providers

We consider the problem faced by a wage-earner with an uncertain lifetime having to reach decisions concerning consumption and life-insurance purchase, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities whose prices are determined by diffusive linear stochastic differential equations. We assume that life-insurance is continuously available for the wage-earner to buy from a market composed of a fixed number of life-insurance companies offering pairwise distinct life-insurance contracts. We characterize the optimal consumption, investment and life-insurance selection and purchase strategies for the wage-earner with an uncertain lifetime and whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming techniques to obtain an explicit solution in the case of discounted constant relative risk aversion (CRRA) utility functions.     

Robust profit opportunities in risky financial portfolios

For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single- and multiple-period settings. We show that the problem of finding the “most robust” profit opportunity can be solved as a convex quadratic programming problem, and investigate its relation to the Sharpe ratio.     

Stochastic regression and its application to hedging in finance

In this paper we investigate how to employ stochastic regression to hedge risks in finance, where the risk of a security is measured by its quadratic variation process. Mykland and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another security. In this paper, we investigate how to further reduce the remaining unhedgable risk by adding more hedging securities. Some practical guidelines on how to choose those hedging securities in practice is also given. Jing’s research was partially supported by Hong Kong RGC (Grant Nos. HKUST6011/07P, HKUST6015/08P), and Zhang’s research was supported in part by National Natural Science Foundation of China (Grant No. 10771214)     

Risk measuring under liquidity risk

We present a general framework for measuring the liquidity risk. The theoretical framework defines risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement model. The liquidity risk is defined as the risk that a security or a portfolio of securities cannot be sold or bought without causing changes in prices. The risk measures are decomposed into two terms, one measuring the risk of the future value of a given position in a security or a portfolio of securities and the other the initial cost of this position. Within the framework of coherent risk measures, the risk measures applied to the random part of the future value of a position in a determinate security are increasing monotonic and convex cash sub-additive on long positions. The contrary, in certain situations, holds for the sell positions. By using convex risk measures, we apply our framework to the situation in which large trades are broken into many small ones. Dual representation results are obtained for both positions in securities and portfolios. We give many examples of risk measures and derive for each of them the respective capital requirement. In particular, we discuss the VaR measure.     

商业银行财务绩效偏序集评价研究

为了提高商业银行财务绩效水平,满足利益相关者信息需求,从收益和风险以及发展的角度构建“盈利性”、“安全性”、“流动性”和“社会性”四个维度的商业银行财务绩效评价指标体系,采用偏序集评价方法对15家样本商业银行2017年财务绩效进行评价。财务绩效排名和HASSE图的结果表明:处于较高层级的样本商业银行财务绩效较好,其盈利性、安全性、流动性较优,并具备较强的发展能力;处于较低层级的样本商业银行财务绩效较差,其盈利性、安全性、流动性较弱,发展能力较弱;重要性程度靠前的 “盈利性”和“安全性”评价维度,不是导致商业银行绩效排名和分层的主要影响因素,商业银行要提升财务绩效,应该更加重视“流动性”和“社会性”维度。同时,采用偏序集评价方法,克服了评价指标精确赋权问题,获得的HASSE图直观展示样本商业银行财务绩效排名稳定性和整体市场竞争格局,具备其他评价方法无法比拟的优势。     

On securitization,market completion and equilibrium risk transfer

We propose an equilibrium framework within which to price financial securities written on non-tradable underlyings such as temperature indices. We analyze a financial market with a finite set of agents whose preferences are described by a convex dynamic risk measure generated by the solution of a backward stochastic differential equation. The agents are exposed to financial and non-financial risk factors. They can hedge their financial risk in the stock market and trade a structured derivative whose payoff depends on both financial and external risk factors. We prove an existence and uniqueness of equilibrium result for derivative prices and characterize the equilibrium market price of risk in terms of a solution to a non-linear BSDE.     

Optimal life insurance purchase,consumption and investment on a financial market with multi-dimensional diffusive terms

We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities driven by multi-dimensional Brownian motion. We then provide a detailed analysis of the optimal consumption, investment and insurance purchase strategies for the wage earner whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming methods to obtain explicit solutions for the case of discounted constant relative risk aversion utility functions and describe new analytical results which are presented together with the corresponding economic interpretations.     

Securitization of catastrophe mortality risks

Securitization with payments linked to explicit mortality events provides a new investment opportunity to investors and financial institutions. Moreover, mortality-linked securities provide an alternative risk management tool for insurers. As a step toward understanding these securities, we develop an asset pricing model for mortality-based securities in an incomplete market framework with jump processes. Our model nicely explains opposite market outcomes of two existing pure mortality securities.     

A multidimensional knapsack model for asset-backed securitization

Securitization is a financial operation which allows a financial institution to transform financial assets, for instance mortgage assets or lease contracts, into marketable securities. We focus the analysis on a real case of a bank for the leasing. Once the securitization characteristics, such as size and times of the operation, have been defined, the profit for the financial institution—Italease Bank for the Leasing in our case—depends on how the financial assets to use in the securitization are selected. We show that the selection problem can be modelled as a multidimensional knapsack problem (MDKP). Some formal arguments suggest that there may exist a prevailing constraint in the MDKP. Such an idea is used in the design of some simple heuristics which turn out to be very effective.     

绝对风险规避者的证券投资理论和方法

本在分析证券投资效用函数的基础上,推导出选择证券投资品种的随机控制准则,特别对三阶随机控制准则的理论和应用做详细分析,并用此准则对上海证券交易所的普通股票作实证分析,这为证券投资选择证券投资品种形成有效证券集合提供科学依据。