Mean-Variance Versus Direct Utility Maximization

Levy and Markowitz showed, for various utility functions and empirical returns distributions, that the expected utility maximizer could typically do very well if he acted knowing only the mean and variance of each distribution. Levy and Markowitz considered only situations in which the expected utility maximizer chose among a finite number of alternate probability distributions. The present paper examines the same questions for a case with an infinite number of alternate distributions, namely those available from the standard portfolio constraint set.     

Note on the Tail Behavior of Random Walk Maxima with Heavy Tails and Negative Drift

Abstract

This paper investigates the asymptotic tail behavior of maxima of a random walk with negative mean and heavy-tailed increment distribution. A simple proof is given to improve the related result in Ng et al. (2002).     

中国国际储备适度规模测度1994～2009——基于效用最大化分析框架的数值模拟

截至2010年9月,中国以美元计价的储备规模已高达2.64万亿美元。储备高速增长增强了中国国际清偿力和抵御国际金融风险的能力,但也会增加国内通货膨胀压力,弱化货币政策的独立性和有效性,成为影响内外均衡的重要问题。本文基于效用最大化分析框架和平滑代表性经济人消费方法,采用1994~2009年度数据分析中国储备规模的变化和适度规模的确定。我们认为,中国储备适度规模/GDP比率的理想变动区间是25%~30%,从2004年开始,实际储备规模超出适度规模平均为10%左右,基本处在合意变动区间内。但从近期储备存量走势来看,适度储备规模缺口存在加速增大的趋势。在储备管理方面,中央银行在运用国际储备进行资金运营和投资时要注意加强对潜在金融风险的监管。     

A Note on International Portfolio Diversification with Short Selling

In this paper, the diversification benefits of using stock index futures are examined. Empirical evidence shows that traditional diversification in international equity markets does not produce a risk adjusted performance superior to the US market. An explanation for this result is that restrictions on short selling prohibit the best allocation of resources when overseas stock markets are riskier and have worse returns. However, when such restrictions are eased for short selling in index futures markets, investors are enabled to both allocate their investments more efficiently and to construct a superior portfolio.     

A Note on Bonus Scales

We revisit the optimal bonus scales introduced by Norberg (Norberg, R., 1976, Scandinavian Actuarial Journal (2): 92‐107), Borgan, Hoem, and Norberg (Borgan, O., J. Hoem, and R. Norberg, 1981, Scandinavian Actuarial Journal (2): 165‐178), and Gilde and Sundt (Gilde, V., and B. Sundt, 1989, Scandinavian Actuarial Journal (1): 13‐22) and underline some potential problems of the linear scales. As a possible solution we propose the use of geometric scales.     

关于Riemann可积性的注记

本文用测度论讨论了一元非连续函数的可积性,给出了一元非连续函数Riemann可积的充分条件.     

一类具有无界时滞的微分不等式

本文建立了一类具有无界时滞微分不等式,将有界时滞微分不等式推广到无界时滞微分不等式,并得到其解的指数估计和渐近估计.     

Mixed Integer Programming Revealed Preference Tests of Utility Maximization and Weak Separability of Consumption,Leisure, and Money

Swofford and Whitney (1987, 1988, 1994) investigated the validity of two key assumptions underlying representative agent models of macroeconomics. These assumptions are utility maximization and weak separability. Using mixed integer programming, we check revealed preference conditions for these assumptions. We find that M1, money defined by Friedman and Schwartz (1963), and a broad aggregate are weakly separable. We find that consumption goods and leisure and nondurables and services are weakly separable. We find that M2, M3, and MZM are not weakly separable. Finally, we find three categories of consumption, durables, nondurables and services, do not form an aggregate.     

最优控制下养老保险多参数改革路径研究

在人口老龄化和人口寿命持续增长的趋势下,大多数实行现收现付制养老保险的国家面临可持续发展的挑战。对于我国基本养老保险的参数式改革,已有量化研究很少同时考虑不同参数之间的关联性和多个参数的综合改革效应。本文针对我国城镇职工基本养老保险,构建了多参数改革的最优化模型,在参数边界和参数连续调整平滑性约束下,通过广义既约梯度法求解制度的缴费率、退休年龄、待遇调整指数的最优连续调整路径。依据测算,只有对三个参数进行综合改革,即对实际缴费率逐步上调,对待遇指数逐步下调,对退休年龄持续推迟,才能在未来50年中实现精算平衡。敏感性分析进一步给出了在不同的初始替代率、工资增长率和利率假设下,最优调整策略的变化路径。本文所构建的多参数综合改革优化模型以及优化求解方法,可以为养老保险改革决策提供重要参考。     

A Note on Deductible Insurance and Production

This paper examines the optimal production decision of a firm facing revenue risk. We show that the purchase of actuarially fair deductible insurance unambiguously induces the firm to produce more if the firm is not only risk averse but also prudent. If the firm's perferences satisfy constant absolute risk aversion, buying actuarially unfair deductible insurance unambiguously enhances production should the positive loading factor be sufficiently small. When there are moral hazard problems in that the firm's output cannot be contracted upon, we show that the purchase of actuarially fair deductible insurance unambiguously induces the firm to produce more if the firm's utility function is quadratic.     

A Note on Interaction between Financial Markets

This paper investigates the interaction between thestock market and the stock option market. When thepredictions of the future stock price distributionsare different between markets,there is a chance that the option pricing method ofBlack and Scholes with its application to anarbitrage trading strategy may lead to substantialmarket turmoil. We will also investigatethe conditions of market stability.     

A Note on Computation of Implied Volatility

This is a note on computation of the implied volatility in theBlack–Scholes formula to evaluate an accuracy of the computation.