Household risk aversion and portfolio choices

In practice, stock investment is one of the most important decisions made by households. The primary goal of this paper is to explain family investment decisions under the assumptions of household member’s preferences and efficient risk sharing based on the collective household model. In particular, by examining the absolute (relative) risk aversion of the household welfare function, we demonstrate how household’s portfolio allocation in stocks changes with family wealth. We examine two types of preference heterogeneity between family members: parameter heterogeneity and functional form heterogeneity. This study offers an alternative explanation of household portfolio choice corresponding with the observation that wealthier households tend to hold greater share of their wealth in risky assets. Specifically, if two decision-makers have standard constant relative risk aversion preference with different relative risk aversions in a household, family’s relative risk aversion decreases as household wealth increases (decreasing relative risk aversion).     

Baseline models are not “finishline” models: A sympathetic critique of Mayhew's strategy

A rationalist view of Relative Deprivation is possible if it is represented with extended preference. In the social movements studies, the concept of relative deprivation has been treated as an intervening variable, which is determined by the interpersonal comparisons and causes the social movements. The most important problem is whether a relatively deprived individual has an incentive for social movements or not. On the one hand he has different reference persons to whom he experiences relative deprivation and a sense of his subjective welfare, which make him behave in respective ways. But on the other hand he can behave in only one way at one time. We formalize the concept of the relative deprivation and construct the model that the relative deprivation and his preference in the ordinary sense are both the factors determining his behavior. Then it is deduced that there's no effect of the feeling relative deprivation for each individual to decide his way under some adequate conditions. So it should be concluded that the concept of the relative deprivation is not effective to explain social movements or social change in collectivities.     

OPTIMAL HARVESTING OF FOREST AGE CLASSES UNDER PRICE UNCERTAINTY AND RISK AVERSION

ABSTRACT. . We analyze optimal forest harvesting under mean reverting and random walk timber price and include multiple age classes, forest owners' consumption‐savings decisions and risk aversion. This framework generalizes existing studies that assume a single stand and risk neutrality or include ad hoc risk aversion and obtain the result that uncertainty lengthens the optimal rotation. Including planting cost implies that price stochasticity may shorten the rotation period. Under the mean reverting price process, optimal harvesting becomes more sensitive to periodic price level, as compared to the random walk case. Including risk aversion completely changes the harvesting policy in the sense that, if the forest initially consists of just one age class, it is optimal to smooth the age class structure and have more frequent cuttings from younger age classes. With risk aversion, optimal cuttings depend on price level, even under a random walk price and zero replanting and harvesting costs. In addition, harvesting decisions become dependent on subjective time preference and forest owners' wealth.     

Own-company stockholding and work effort preferences of an unconstrained executive

We develop a framework for analyzing an executive’s own-company stockholding and work effort preferences. The executive, characterized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive’s utility-maximizing personal investment and work effort strategy is derived in closed form, and a utility indifference rationale is applied to determine his required compensation. Being unconstrained by performance contracting, the executive’s work effort strategy establishes a base case for theoretical or empirical assessment of the benefits or otherwise of constraining executives with performance contracting.     

Zero-Level Pricing and the HARA Utility Functions

In the mathematical economics literature, the zero-level pricing method has been proposed to provide a unique price for a nonmarketable new asset. From the viewpoint of robust pricing theory, its disadvantage is that the method depends on the investor utility function and initial wealth. In some situations, the zero-level price is universal, namely, independent of the utility function and initial wealth. We show that only one parameter of the HARA (hyperbolic absolute risk aversion) utility function affects the zero-level price of a new asset. This implies that, if this parameter is fixed, the zero-level price is identical for all individuals with HARA utility functions and different levels of initial wealth. This research was partially supported by Grant NSC 95-2221-E-155-049.     

On expected utility for financial insurance portfolios with stochastic dependencies

The effect of background risks as human capital, market risks and catastrophic events has been considered in the literature in different contexts. In this note, we consider financial insurance portfolios with insurable risks and one background risk (uninsurable financial asset), such that the random losses and the background risk depend on environmental parameters. We study how dependencies between the risks influence the expected utility of the portfolio’s wealth distribution under risk aversion, when the environmental parameters are random. Stochastic bounds for the expected wealth are given from modeling the dependence between the parameters by different notions. Similar results are given for multivariate portfolios with n groups and multivariate risk aversion, besides an expected utility comparison result for the minimum and the total portfolio’s wealth.     

Optimal portfolio, consumption and retirement decision under a preference change

We investigate an optimal portfolio, consumption and retirement decision problem in which an economic agent can determine the discretionary stopping time as a retirement time with constant labor wage and disutility. We allow the preference of the agent to be changed before and after retirement. It is assumed that the agent's coefficient of relative risk aversion becomes higher after retirement. Under a constant relative risk aversion (CRRA) utility function, we obtain the optimal policies in closed-forms using martingale methods and variational inequality methods. We give some numerical results of the optimal policies. We also consider the relation between the level of disutility and the labor wage with the optimal retirement wealth level.     

Reinsurance contract design when the insurer is ambiguity-averse

This paper investigates proportional and excess-loss reinsurance contracts in a continuous-time principal–agent framework, in which the insurer is the agent and the reinsurer is the principal. Insurance claims follow the classic Cramér–Lundberg process. The insurer believes that the claim intensity is uncertain and he chooses robust risk retention levels to maximize the penalty-dependent multiple-priors utility. The reinsurer designs reinsurance contracts subject to the insurer’s incentive compatibility constraints. The analytical expressions of the two robust reinsurance contracts are derived. Our results show that the robust reinsurance demand and price are greater than their respective standard values without model ambiguity, and increase as the insurer’s ambiguity aversion increases. Moreover, the reinsurer specifies a decreasing reinsurance price to induce increasing demand over time. Specifically, the price of excess-loss reinsurance is higher, relative to that of proportional reinsurance. Further, only if the insurer’s risk aversion is high or the reinsurer’s risk aversion is low, the insurer prefers the excess-loss reinsurance contract.     

On perfectly homogeneous bases in Banach spaces

It is proved that a Banach space is isomorphic toc _o or tol _p if and only if it has a normalized basis {χ_i i _{} i=1} ^∞ which is equivalent to every normalized block-basis with respect to {χ_i i _{} i=1} ^∞ . This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Prof. A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful guidance and for the interest he showed in the paper, and the referee for his valuable remakrs.     

Background risk,bivariate risk attitudes,and optimal prevention

This paper extends Eeckhoudt et al.’s (2012) results for precautionary effort to bivariate utility function framework. We establish an equivalence between the agent’s precautionary effort motive and the signs of successive cross-derivatives of the bivariate utility function. We show that the introduction (or deterioration) of an independent background risk induces more prevention to protect against wealth loss provided the individual exhibits correlation aversion of some given order. The conditions on the individual’s risk preferences are given to generate some specific prevention behaviors in the univariate framework with multiplicative risks. Our conclusion also indicates that an increase in the correlation between wealth risk and background risk leads to a reduction in optimal prevention.     

Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump–diffusion model

In this paper, we study an optimal investment problem under the mean–variance criterion for defined contribution pension plans during the accumulation phase. To protect the rights of a plan member who dies before retirement, a clause on the return of premiums for the plan member is adopted. We assume that the manager of the pension plan is allowed to invest the premiums in a financial market, which consists of one risk-free asset and one risky asset whose price process is modeled by a jump–diffusion process. The precommitment strategy and the corresponding value function are obtained using the stochastic dynamic programming approach. Under the framework of game theory and the assumption that the manager’s risk aversion coefficient depends on the current wealth, the equilibrium strategy and the corresponding equilibrium value function are also derived. Our results show that with the same level of variance in the terminal wealth, the expected optimal terminal wealth under the precommitment strategy is greater than that under the equilibrium strategy with a constant risk aversion coefficient; the equilibrium strategy with a constant risk aversion coefficient is revealed to be different from that with a state-dependent risk aversion coefficient; and our results can also be degenerated to the results of He and Liang (2013b) and Björk et al. (2014). Finally, some numerical simulations are provided to illustrate our derived results.     

A Note on K-Theory of Azumaya Algebras

For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that K _i (A, ?/m) = K _i (R, ?/m) for any m relatively prime to the rank and i ≥ 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semilocal rings, and K-theory of graded central simple algebras indexed by a totally ordered abelian group.     

Indifference pricing for CRRA utilities

We study utility indifference pricing of claim streams with intertemporal consumption and constant relative risk aversion utilities. We derive explicit formulas for the derivatives of the utility indifference price with respect to claims and wealth. The elegant structure of these formulas is a reflection of surprising algebraic identities for the derivatives of the optimal consumption stream. Namely, the partial derivative of the optimal consumption stream with respect to the endowment is always a projection. Furthermore, it is an orthogonal projection with respect to a natural “economic inner product”. These algebraic identities generate cancellations between the terms entering derivatives of the indifference price and allow us to prove sharp global bounds for the indifference price that become exact when the claims to wealth ratio is large and risk aversion is between one and two. For general risk aversion, we show that, in the large claims to wealth ratio limit, the asymptotic expansion of the indifference price is given in terms of fractional powers of the wealth, depending on risk aversion. When risk aversion is equal to one, the fractional power depends on the underlying claim.     

Utility maximization, risk aversion, and stochastic dominance

Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the optimal terminal payoff. Economic intuition suggests that high risk aversion leads to a rather concentrated distribution, whereas lower risk aversion results in a higher average payoff at the expense of a more widespread distribution. Dybvig and Wang (J. Econ. Theory, 2011, to appear) find that this idea can indeed be turned into a rigorous mathematical statement in one-period models. More specifically, they show that lower risk aversion leads to a payoff which is larger in terms of second order stochastic dominance. In the present study, we extend their results to (weakly) complete continuous-time models. We also complement an ad-hoc counterexample of Dybvig and Wang, by showing that these results are “fragile”, in the sense that they fail in essentially any model, if the latter is perturbed on a set of arbitrarily small probability. On the other hand, we establish that they hold for power investors in models with (conditionally) independent increments.     

基于委托代理理论的“公司+农户”租赁模式分析

针对公司与农户合作时存在违约问题,本文基于委托代理理论构建了由风险规避的公司和农户组成的“公司+农户”租赁模型。分析了在信息不对称条件下,该模式的激励系数与租金的制定策略,并通过数值仿真探讨了各参数变化对激励系数和租金的影响。研究结果表明公司给予农户的分成比例越高,农户生产努力水平越高,同时公司前期支付给农户的租金越低,后期给予农户的分成比例越高。此外,激励系数随公司风险规避系数、农户生产能力的增加而增加,随农户风险规避系数、外生不确定因素的增加而减小;租金随农户风险规避系数、农户生产能力的增加而增加,随公司风险规避系数、外生不确定因素的增加而减小,并且在满足一定条件时,存在最优的市场价格使得租金最低。     

Optimal portfolio choice and stochastic volatility

In this paper we examine the effect of stochastic volatility on optimal portfolio choice in both partial and general equilibrium settings. In a partial equilibrium setting we derive an analog of the classic Samuelson–Merton optimal portfolio result and define volatility‐adjusted risk aversion as the effective risk aversion of an individual investing in an asset with stochastic volatility. We extend prior research which shows that effective risk aversion is greater with stochastic volatility than without for investors without wealth effects by providing further comparative static results on changes in effective risk aversion due to changes in the distribution of volatility. We demonstrate that effective risk aversion is increasing in the constant absolute risk aversion and the variance of the volatility distribution for investors without wealth effects. We further show that for these investors a first‐order stochastic dominant shift in the volatility distribution does not necessarily increase effective risk aversion, whereas a second‐order stochastic dominant shift in the volatility does increase effective risk aversion. Finally, we examine the effect of stochastic volatility on equilibrium asset prices. We derive an explicit capital asset pricing relationship that illustrates how stochastic volatility alters equilibrium asset prices in a setting with multiple risky assets, where returns have a market factor and asset‐specific random components and multiple investor types. Copyright © 2011 John Wiley & Sons, Ltd.     

On the rank of the fibers of elliptic K3 surfaces

Let X be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations π _i , i = 1, 2, defined over a number field k. We prove that there is an elliptic curve C ⊂ X such that the generic rank over k of X after a base extension by C is strictly larger than the generic rank of X. Moreover, if the generic rank of π _j is positive then there are infinitely many fibers of π _i (j ≠ i) with rank at least the generic rank of π _i plus one.     

Optimal Basket Liquidation for CARA Investors is Deterministic

Abstract

We consider the problem faced by an investor who must liquidate a given basket of assets over a finite time horizon. The investor's goal is to maximize the expected utility of the sales revenues over a class of adaptive strategies. We assume that the investor's utility has constant absolute risk aversion (CARA) and that the asset prices are given by a very general continuous-time, multiasset price impact model. Our main result is that (perhaps surprisingly) the investor does no worse if he narrows his search to deterministic strategies. In the case where the asset prices are given by an extension of the nonlinear price impact model of Almgren [(2003) Applied Mathematical Finance, 10, pp. 1–18], we characterize the unique optimal strategy via the solution of a Hamilton equation and the value function via a nonlinear partial differential equation with singular initial condition.