Adaptive utility and trial aversion

Decision making with adaptive utility provides a generalisation to classical Bayesian decision theory, allowing the creation of a normative theory for decision selection when preferences are initially uncertain. In this paper we address some of the foundational issues of adaptive utility as seen from the perspective of a Bayesian statistician. The implications that such a generalisation has upon the traditional utility concepts of value of information and risk aversion are also explored, with a new concept of trial aversion introduced that is similar to risk aversion, but which concerns a decision maker's aversion to selecting decisions with high uncertainty over resulting utility.     

Optimal consumption and portfolio selection with negative wealth constraints,subsistence consumption constraints,and CARA utility

We consider the optimal consumption and portfolio selection problem with constant absolute risk aversion (CARA) utility. The economic agent in this model receives constant labor income, and her economic behavior is restricted on consumption and wealth, which are called the subsistence consumption constraint and the negative wealth constraint. We use the convex duality method to derive the value function and the optimal policies in closed-form solutions. Also we illustrate some numerical examples.     

Asset Prices Under Habit Formation and Reference-Dependent Preferences

This article explains the high level and the countercyclical variation of the equity premium in a consumption-based asset pricing model with low large-scale risk aversion. Investors have gain-loss utility over consumption relative to slowly time-varying habit. Stocks deliver low returns in recessions when consumption falls below habit; investors therefore require a high premium for holding stocks. The model's conditional moment restrictions are tested on consumption and asset returns data. The empirical estimate of large-scale risk aversion is low, whereas the estimate of loss aversion agrees with prior experimental evidence.     

RISK PREFERENCES UNDER PRICE UNCERTAINTIES AND PRODUCTION RISK

This paper deals with estimation of risk preferences of producers when they face uncertainties in output and input prices, in addition to uncertainty in production (usually labeled as production risk). All these uncertainty components are modeled in the context of production theory where the producers maximize expected utility of anticipated profit. Risk preference functions associated with these uncertainties are derived without assuming a specific form of the utility function. Moreover, no distributional assumptions are made on the distributions of the random variables representing price and production uncertainties. A multi-stage estimation procedure is developed to estimate the parameters of the production function and risk preference functions associated with output price uncertainty, input price uncertainty and production risk. Production risk is specified in such a way that one can identify inputs with increasing, decreasing and constant production risks. Similarly, risk aversion behavior is specified in such a way that one can test for different types of risk aversion behavior.     

Optimal investment and consumption with unknown parameters

An investment and consumption problem is formulated and its optimal strategy is investigated. We assume the basic binary model, but with unknown parameters. We apply the parametric Bayesian approach to formulate the problem as a sequential stochastic optimization model and use the technique of dynamic programming to characterize the optimal strategy. It is discovered that despite unknown parameters, when the power and logarithmic utility functions are treated, the optimal value function is of the same form of the utility function. The random finite horizon model is formulated as an infinite horizon model. Our results are similar to the ones in the literature having different return functions with constant relative risk aversion.     

Ambiguity in the Cross-Section of Expected Returns: An Empirical Assessment

This article estimates and tests the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji based on stock market data. We introduce a novel methodology to estimate the conditional expectation, which characterizes the impact of a decision maker’s ambiguity attitude on asset prices. Our point estimates of the ambiguity parameter are between 25 and 60, whereas our risk aversion estimates are considerably lower. The substantial difference indicates that market participants are ambiguity averse. Furthermore, we evaluate if ambiguity aversion helps explaining the cross-section of expected returns. Compared with Epstein and Zin preferences, we find that incorporating ambiguity into the decision model improves the fit to the data while keeping relative risk aversion at more reasonable levels. Supplementary materials for this article are available online.     

信贷约束、风险态度与家庭资产选择

本文运用中国家庭金融调查数据（CHFS）,从信贷约束与风险态度两个方面研究其对家庭资产的参与及配置影响。研究发现,在控制其他因素情况下,家庭信贷约束会增加家庭风险厌恶程度;受到信贷约束的家庭,其房产持有概率和房产市值均显著下降;其股票持有概率会显著下降,但对其持有股票市值影响并不显著;受到信贷约束的家庭,其购买商业保险的概率偏低;家庭风险态度对家庭房产选择的影响不显著;对股票资产的持有概率和持有量均产生负向影响,对商业保险资产的持有则产生显著正向影响。     

风险规避情形下第一价格拍卖的非参数估计方法

在拍卖实证研究的大量文献中,越来越多的证据表明投标人更趋向于风险规避,然而目前拍卖计量方法通常只考虑风险中性的情形。针对这一问题,推广了针对第一价格拍卖的非参数估计方法,给出了多个风险规避参数估计量来处理风险规避的情形,并总结了相应的估计过程。为验证估计效果,蒙特卡罗模拟实验被用于进行分析和评价。实验结果表明,无论是对风险规避参数,还是私有估值的估计,总体上都能取得不错的效果,验证了方法的有效性,同时为风险规避参数估计量的选择提供了一些指导性建议。     

A functional coefficient GARCH-M model

ABSTRACT

Motivated by the time varying property of the risk aversion and the functional coefficient regression model, a functional coefficient GARCH-M model is studied. The proposed GARCH-M type model gives a way to study the relationship between risk aversion and certain variable. An approach is given to estimate the model and some theoretical results are obtained. Simulations demonstrate that the method performs well. From the empirical studies, it is shown that the proposed model can better fit the considered data compared to the usual parametric models.     

Robust portfolio choice for a defined contribution pension plan with stochastic income and interest rate

This paper considers a robust portfolio choice problem for a defined contribution pension plan with stochastic income and stochastic interest rate. The investment objective of the pension plan is to maximize the expected utility of the wealth at the retirement time. We assume that the financial market consists of a stock, a zero-coupon bond and a risk-free asset. And the member of defined contribution pension plan is ambiguity-averse, which means that the member is uncertain about the expected return rate of the bond and stock. Meanwhile, the member's ambiguity-aversion level toward these two financial assets is quite different. The closed-form expressions of the robust optimal investment strategy and the corresponding value function are derived by adopting the stochastic dynamic programming approach. Furthermore, the sensitive analysis of model parameters on the optimal investment strategy are presented. We find that the member's aversion on model ambiguity increases her hedging demand and has remarkable impact on the optimal investment strategy. Moreover, we demonstrate that ignoring model uncertainty will lead to significant utility loss for the ambiguity-averse member, and the model uncertainty about the stock dynamics implies greater effect on the outcome of the investment than the bond.     

Using the Standardized Difference to Compare the Prevalence of a Binary Variable Between Two Groups in Observational Research

Researchers are increasingly using the standardized difference to compare the distribution of baseline covariates between treatment groups in observational studies. Standardized differences were initially developed in the context of comparing the mean of continuous variables between two groups. However, in medical research, many baseline covariates are dichotomous. In this article, we explore the utility and interpretation of the standardized difference for comparing the prevalence of dichotomous variables between two groups. We examined the relationship between the standardized difference, and the maximal difference in the prevalence of the binary variable between two groups, the relative risk relating the prevalence of the binary variable in one group compared to the prevalence in the other group, and the phi coefficient for measuring correlation between the treatment group and the binary variable. We found that a standardized difference of 10% (or 0.1) is equivalent to having a phi coefficient of 0.05 (indicating negligible correlation) for the correlation between treatment group and the binary variable.     

A theoretical basis for perturbation methods

In this paper we discuss a new theoretical basis for perturbation methods. In developing this new theoretical basis, we define the ideal measures of data utility and disclosure risk. Maximum data utility is achieved when the statistical characteristics of the perturbed data are the same as that of the original data. Disclosure risk is minimized if providing users with microdata access does not result in any additional information. We show that when the perturbed values of the confidential variables are generated as independent realizations from the distribution of the confidential variables conditioned on the non-confidential variables, they satisfy the data utility and disclosure risk requirements. We also discuss the relationship between the theoretical basis and some commonly used methods for generating perturbed values of confidential numerical variables.     

Optimal asset allocation for participating contracts with mortality risk under minimum guarantee

Abstract

We investigate an optimal investment problem of participating insurance contracts with mortality risk under minimum guarantee. The insurer aims to maximize the expected utility of the terminal payoff. Due to its piecewise payoff structure, this optimization problem is a non-concave utility maximization problem. We adopt a concavification technique and a Lagrange dual method to solve the problem and derive the representations of the optimal wealth process and trading strategies. We also carry out some numerical analysis to show how the portfolio insurance constraint impacts the optimal terminal wealth.     

农村居民消费增长比平稳更重要

 本文将消费习惯引入Lucas (1987)模型,采用农村五等份收入户的人均消费数据进行数值模拟,结果发现: 消费增长比消费平稳更重要,且收入等级越高,这种相对重要性就越突出。相对风险规避系数一定时,两类福利成本之比随习惯强度变化的轨迹呈倒U型; 习惯强度一定时,两类福利成本之比随相对风险规避系数的增大而递减。相对于其他等级的收入户,促进消费增长的经济政策为高收入户带来相对较多的福利,而平抑消费波动的经济政策能为低收入户带来较多的福利。因此,政府在促进农村居民消费增长的同时,也应重视消费波动给低收入群体造成的福利成本。     

An optimal investment and risk control policy for a bank under exponential utility

Motivated by the Basel Capital Accord Requirement (CAR), we analyze a risk control portfolio selection problem under exponential utility when a banker faces both Brownian and jump risks. The banker's risk process and the dynamics of the risky asset process are modeled as jump-diffusion processes. Assuming that the constraint set of all trading strategies is in a closed set, we study the terminal utility optimization problem via the backward stochastic differential equation (BSDE) under risk regulation paradigm. We construct the BSDE by means of the martingale optimality principle, giving conditions for the corresponding generator to be well defined in order to derive the bounds on the candidate optimal strategy. We then construct an internal model for the bank under Basel III CAR, which is formulated from the total risk-weighted assets (TRWA's) and bank capital. The results obtained from this model can be adopted within the banking sector when setting up asset investment strategies and advanced risk management models, as advocated by the Basel III Accord.     

The Role of Heterogeneity in Asset Pricing: The Effect of a Clustering Approach

In this article we use a novel clustering approach to study the role of heterogeneity in asset pricing. We present evidence that the equity premium is consistent with a stochastic discount factor (SDF) calculated as the average of the household clusters’ intertemporal marginal rates of substitution in the 1984–2002 period. The result is driven by the skewness of the cluster-based cross-sectional distribution of consumption growth, but cannot be explained by the cross-sectional variance and mean alone. We find that nine clusters are sufficient to explain the equity premium with relative risk aversion coefficient equal to six. The result is robust to various averaging schemes of cluster-based consumption growth used to construct the SDF. Lastly, the analysis reveals that standard approximation schemes of the SDF using individual household data produce unreliable results, implying a negative SDF.     

Micro-Level Estimation of Optimal Consumption Choice With Intertemporal Nonseparability in Preferences and Measurement Errors

This article investigates the presence of habit formation in household consumption, using data from the Panel Study of Income Dynamics. We develop an econometric model of internal habit formation of the multiplicative specification. The restrictions of the model allow for classical measurement errors in consumption without parametric assumptions on the distribution of measurement errors. We estimate the parameters by nonlinear generalized method of moments and find that habit formation is an important determinant of household food-consumption patterns. Using the parameter estimates, we develop bounds for the expectation of the implied heterogenous intertemporal elasticity of substitution and relative risk aversion that account for measurement errors, and compute confidence intervals for these bounds. Supplementary materials for this article are available online.     

Estimating the Continuous-Time Consumption-Based Asset-Pricing Model

The consumption-based asset-pricing model predicts that excess yields are determined by the market's degree of relative risk aversion and by the covariances of per capita consumption growth with asset returns. Estimation and testing are complicated by the fact that the model's predictions relate to the instantaneous flow of consumption and point-in-time asset values, but only data on the integral or time average of the consumption flow are available. This article shows how to take account of the effects of time averaging on the covariances. We estimate the model's parameters and test the overidentifying restrictions using six different data sets.     

Automating and evaluating reversible jump MCMC proposal distributions

The reversible jump Markov chain Monte Carlo (MCMC) sampler (Green in Biometrika 82:711–732, 1995) has become an invaluable device for Bayesian practitioners. However, the primary difficulty with the sampler lies with the efficient construction of transitions between competing models of possibly differing dimensionality and interpretation. We propose the use of a marginal density estimator to construct between-model proposal distributions. This provides both a step towards black-box simulation for reversible jump samplers, and a tool to examine the utility of common between-model mapping strategies. We compare the performance of our approach to well established alternatives in both time series and mixture model examples.     

Understanding the Risk-Return Relation: The Aggregate Wealth Proxy Actually Matters

ABSTRACT

The ICAPM implies that the market’s conditional expected return is proportional to its conditional variance and that the reward-to-risk ratio equals the representative investor’s coefficient of relative risk aversion. Prior studies examine this relation using the stock market to proxy for aggregate wealth and find mixed results. We show, however, that stock-based tests suffer from low power and lead to biased estimates of the risk-return tradeoff when stocks are an imperfect market proxy. Tests designed to mitigate this bias by incorporating a more comprehensive measure of aggregate wealth produce large, positive estimates of the risk-aversion coefficient around seven to nine. Supplementary materials for this article are available online.