AN OBTRUSIVE REMARK ON CAPITAL AND COMPARATIVE STATICS

We present a simple comparative statics analysis of steady‐state equilibria in overlapping generations economies with capital accumulation. We regard comparative statics as paradoxical whenever an exogenous increase in saving propensity induces a decrease (an increase) in consumption at the steady state when interest rate is positive (negative). It is shown that there is an exact relation between paradoxical comparative statics and a perverse intersection of properly identified curves of demand for and supply of capital in value. The demand curve for capital in value coincides with that of neo‐Ricardian analysis. We relate our conclusions to some old and recent issues in capital theory.     

LONG RUN DEMAND FOR LABOUR IN THE CONSUMER GOOD INDUSTRY

We consider, for alternative models of production, the comparative statics of constant‐returns economies in long run competitive equilibrium, for which reswitching, capital‐reversing and consumption‐reversal are all completely absent. Notwithstanding the ‘well‐behaved’ nature of these economies, the use of labour per unit of output in the consumer good industry is always positively related to the real wage rate.     

Consumer Substitution Effects under Full Industry Equilibrium

To be of practical use comparative statics must be able to compare long‐period equilibria. Such equilibria will almost never have price vectors that are proportional with respect to all prices but one—yet such price vectors are precisely those underlying the usual substitution effect analysis. We consider how this tension may be resolved.     

Optimal insurance under rank‐dependent utility and incentive compatibility

Bernard, He, Yan, and Zhou (Mathematical Finance, 25(1), 154–186) studied an optimal insurance design problem where an individual's preference is of the rank‐dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their results suffer from the unrealistic assumption that the random loss has no atom, as well as a problem of moral hazard that provides incentives for the insured to falsely report the actual loss. This paper addresses these setbacks by removing the nonatomic assumption, and by exogenously imposing the “incentive compatibility” constraint that both indemnity function and insured's retention function are increasing with respect to the loss. We characterize the optimal solutions via calculus of variations, and then apply the result to obtain explicitly expressed contracts for problems with Yaari's dual criterion and general RDU. Finally, we use numerical examples to compare the results between ours and Bernard et al.     

Credit portfolio selection with decaying contagion intensities

We develop a fixed‐income portfolio framework capturing the exponential decay of contagious intensities between successive default events. We show that the value function of the control problem is the classical solution to a recursive system of second‐order uniformly parabolic Hamilton–Jacobi–Bellman partial differential equations. We analyze the interplay between risk premia, decay of default intensities, and their volatilities. Our comparative statics analysis finds that the investor chooses to go long only if he is capturing enough risk premia. If the default intensities deteriorate faster, the investor increases the size of his position if he goes short, or reduces the size of his position if he goes long.     

THE EFFECT OF ESTIMATION IN HIGH‐DIMENSIONAL PORTFOLIOS

We study the effect of estimated model parameters in investment strategies on expected log‐utility of terminal wealth. The market consists of a riskless bond and a potentially vast number of risky stocks modeled as geometric Brownian motions. The well‐known optimal Merton strategy depends on unknown parameters and thus cannot be used in practice. We consider the expected utility of several estimated strategies when the number of risky assets gets large. We suggest strategies which are less affected by estimation errors and demonstrate their performance in a real data example. Strategies in which the investment proportions satisfy an L₁ ‐constraint are less affected by estimation effects.     

A MICROECONOMIC MODEL OF CORPORATE SOCIAL RESPONSIBILITY

This paper explores the economic mechanisms behind corporate social responsibility (CSR) in a microeconomic model of the firm. The study's motivation is to shed light on the potential causes of the observed phenomena of voluntary over‐compliance among firms. We investigate how assumptions about costs and benefits affect CSR behavior through a stock of goodwill capital. In optimum, the firm must balance marginal costs and benefits of investing in CSR. We characterize the equilibrium and examine comparative statics and dynamics from a parameterized model. Finally, we link some of the model's results to the empirical literature on CSR.     

Balance‐of‐payments‐constrained cyclical growth with distributive class conflicts and productivity dynamics

This study builds a dynamic balance‐of‐payments‐constrained model that incorporates the endogenous determination of the economic growth rate, conflictive wage/price distribution and employment rate. The wages, commodity prices and employment rate are determined by the profit squeeze effect and labour‐saving technical change. The relative strength of these two effects generates different outcomes for the transitional dynamics and comparative statics analysis. Particularly, the model shows stability, instability and cyclical nature, the latter of which concurs with the evidence reported by previous empirical studies.     

Capped equity swaps under the double‐jump stochastic volatility model with stochastic interest rates

This study proposes a double‐jump stochastic volatility model with stochastic interest rates to price capped equity swaps and other multi‐period derivative securities. Closed‐form solutions for capped equity swaps with a fixed or variable notional principle are derived. In addition, numerical examples are employed to analyze comparative statics properties, counterparty risks, and the dynamics of the forward smile. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:340–370, 2011     

Too many options? Theory and evidence on option exchange design

A model of option exchange design is proposed and tested. The model allows investors to choose among several exchange‐traded options based on a trade‐off between standardization costs and liquidity/transaction costs. It employs a spatial economics approach to provide results for the existence of markets for particular option contracts on the exchange, a comparison of exchange design by a social planner and a profit‐maximizing monopolist (corresponding to the idea that most derivatives exchanges centralize the design and creation of option contracts), and comparative statics that can potentially aid decision makers in the design of option exchanges. In the empirical work, open interest is analyzed for Chicago Board Options Exchange (CBOE) options on the stocks in the S&P 100 index. In accordance with the model's predictions, open interest forms a previously undocumented seesaw pattern across strike prices, clustering around certain strike prices, and dropping off for the adjacent strike prices. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:533–570, 2006     

Optimal consumption and investment with liquid and illiquid assets

I consider an optimal consumption/investment problem to maximize expected utility from consumption. In this market model, the investor is allowed to choose a portfolio that consists of one bond, one liquid risky asset (no transaction costs), and one illiquid risky asset (proportional transaction costs). I fully characterize the optimal consumption and trading strategies in terms of the solution of the free boundary ordinary differential equation (ODE) with an integral constraint. I find an explicit characterization of model parameters for the well‐posedness of the problem, and show that the problem is well posed if and only if there exists a shadow price process. Finally, I describe how the investor's optimal strategy is affected by the additional opportunity of trading the liquid risky asset, compared to the simpler model with one bond and one illiquid risky asset.     

MULTIPLICATIVE APPROXIMATION OF WEALTH PROCESSES INVOLVING NO‐SHORT‐SALES STRATEGIES VIA SIMPLE TRADING

A financial market model with general semimartingale asset–price processes and where agents can only trade using no‐short‐sales strategies is considered. We show that wealth processes using continuous trading can be approximated very closely by wealth processes using simple combinations of buy‐and‐hold trading. This approximation is based on controlling the proportions of wealth invested in the assets. As an application, the utility maximization problem is considered and it is shown that optimal expected utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well by the use of simple combinations of buy‐and‐hold strategies.     

Bond Rate,Loan Rate and Tobin's q in a Temporary Equilibrium Model of the Financial Sector

The paper sets up a portfolio model of the financial sector with markets for equity, government bonds, money and debt. The comparative statics of the temporary equilibrium are studied analytically and numerically. Subsequent simulations explore the reactions of financial markets in response to stylized oscillations of some of the exogenous variables. These include economic activity, income distribution, inflation, investors' sentiment, and banks' perceived bankruptcy risk of firms. Special emphasis is put on the resulting cyclical pattern of Tobin's q and the interest spread between loan rate and bond rate.     

Rybczynski's Theorem in the Heckscher-Ohlin World — Anything Goes

We demonstrate that Rybczynski's classic comparative statics can be reversed in a Heckscher-Ohlin world when preferences in each country favor the exported commodity. This taste bias has empirical support. An increase in the endowment of a factor of production can lead to an absolute curtailment in the production of the commodity using that factor intensively, and an absolute expansion of the commodity using relatively little of the same factor. This outcome - which we call “Reverse Rybczynski” - implies immiserizing factor growth. We present a simple analytical example that delivers this result with unique pre- and post-growth equilibria. In this example, production occurs within the cone of diversification, such that factor price equalization holds. We also provide general conditions that determine the sign of Rybczynski's comparative statics.     

贸易自由化福利收益模型和我国服务贸易发展的现实选择

通过构建福利收益模型,将服务贸易自由化和货物贸易自由化的收益进行比较,可得出如下结论:服务贸易自由化比货物贸易自由化的收益大。以发展服务贸易为主,实现服务贸易的自由化是贸易自由化发展的高级阶段,但我国目前的服务贸易发展水平还不具备这种条件。针对我国服务贸易及服务业中存在的问题,本文为提高服务贸易竞争力、促进服务贸易自由化提出了相应的政策建议。     

Gravity in International Finance

The past decade has witnessed an explosion of papers estimating gravity equations for cross-border financial holdings without much of a theoretical foundation. In this paper we develop a theory for bilateral asset holdings that takes a gravity form. We discuss how to estimate international financial frictions and conduct comparative statics analysis within the context of the theory. We also find though that reasonable extensions of the model no longer generate a gravity form. While this does not significantly complicate estimation and comparative statics analysis, it raises questions about the empirical validity of gravity specifications for cross-border financial holdings that need to be addressed in future work.     

Convergence of optimal expected utility for a sequence of discrete‐time markets

We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The nth discrete‐time economy is generated by a scaled n‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support. We confirm Kreps' conjecture if the consumer's utility function U has asymptotic elasticity strictly less than one, and we provide a counterexample to the conjecture for a utility function U with asymptotic elasticity equal to 1, for ζ such that .     

A NOTE ON THE QUANTILE FORMULATION

Many investment models in discrete or continuous‐time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original investment problem. Under certain monotonicity assumptions, several schemes to solve such quantile optimization problems have been proposed in the literature. In this paper, we propose a change‐of‐variable and relaxation method to solve the quantile optimization problems without using the calculus of variations or making any monotonicity assumptions. The method is demonstrated through a portfolio choice problem under rank‐dependent utility theory (RDUT). We show that this problem is equivalent to a classical Merton's portfolio choice problem under expected utility theory with the same utility function but a different pricing kernel explicitly determined by the given pricing kernel and probability weighting function. With this result, the feasibility, well‐posedness, attainability, and uniqueness issues for the portfolio choice problem under RDUT are solved. It is also shown that solving functional optimization problems may reduce to solving probabilistic optimization problems. The method is applicable to general models with law‐invariant preference measures including portfolio choice models under cumulative prospect theory (CPT) or RDUT, Yaari's dual model, Lopes' SP/A model, and optimal stopping models under CPT or RDUT.     

Liquidity risk and the hedging role of options

This study examines the impact of liquidity risk on the behavior of the competitive firm under price uncertainty in a dynamic two‐period setting. The firm has access to unbiased one‐period futures and option contracts in each period for hedging purposes. A liquidity constraint is imposed on the firm such that the firm is forced to terminate its risk management program in the second period whenever the net loss due to its first‐period hedge position exceeds a predetermined threshold level. The imposition of the liquidity constraint on the firm is shown to create perverse incentives to output. Furthermore, the liquidity constrained firm is shown to purchase optimally the unbiased option contracts in the first period if its utility function is quadratic or prudent. This study thus offers a rationale for the hedging role of options when liquidity risk prevails. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:789–808, 2006     

OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITY

We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank‐dependent expected utility (RDEU) theory with a concave utility function and an inverse‐S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.