指数风险偏好下的最优保险策略

本文讨论了当投保个体和保险公司为指数风险偏好时，在保费约束下投保个体的最优保险策略问题。本文采用求解对偶优化问题的方法求解这个问题，并给出当损失服从指数分布时最优保险策略解的解析式。本文最后讨论了投保个体和保险公司风险厌恶程度以及保费预算变化对个体最优保险策略的影响。     

Arbitrage, linear programming and martingales¶in securities markets with bid-ask spreads

In a general, finite-dimensional securities market model with bid-ask spreads, we characterize absence of arbitrage opportunities both by linear programming and in terms of martingales. We first show that absence of arbitrage is equivalent to the existence of solutions to the linear programming problems that compute the minimum costs of super-replicating the feasible future cashflows. Via duality, we show that absence of arbitrage is also equivalent to the existence of underlying frictionless (UF) state-prices. We then show how to transform the UF state-prices into state-price densities, and use them to characterize absence of arbitrage opportunities in terms of existence of a securities market with zero bid-ask spreads whose price process lies inside the bid-ask spread. Finally, we argue that our results extend those of Naik (1995) and Jouini and Kallal (1995) to the case of intermediate dividend payments and positive bid-ask spreads on all assets.     

Core and competitive equilibria: An approach from discrete convex analysis

We extend the assignment market (Shapley and Shubik, 1972; Kaneko, 1976, 1982) by utilizing discrete convex analysis. We consider the market in which buyers and sellers trade indivisible commodities for money. Each buyer demands at most one unit of commodity. Each seller produces multiple units of several types of commodities. We make the quasi-linearity assumption on the sellers, but not on the buyers. We assume that the cost function of each seller is M^♮-convex, which is a concept in discrete convex analysis. We prove that the core and the competitive equilibria exist and coincide in our market model.     

Indivisible commodities and the nonemptiness of the weak core

We consider a sufficient condition for the nonemptiness of the weak core in a finite exchange economy where every commodity is available only in integer quantities. We show that if the aggregate upper contour set is discretely convex, then the weak core is nonempty. In addition, we give two sufficient conditions for the aggregate upper contour set to be discretely convex. One is that every upper contour set of every agent is M^?${\text{M}}^{?}$-convex. The other is that the number of commodities is two and every agent’s preference relation is weakly monotone and discretely convex.     

No arbitrage conditions and liquidity

We extend the fundamental theorem of asset pricing to the case of markets with liquidity risk. Our results generalize, when the probability space is finite, those obtained by Kabanov et al. [Kabanov, Y., Stricker, C., 2001. The Harrison-Pliska arbitrage pricing theorem under transaction costs. Journal of Mathematical Economics 35, 185–196; Kabanov, Y., Rásonyi, M., Stricker, C., 2002. No-arbitrage criteria for financial markets with efficient friction. Finance and Stochastics 6, 371–382; Kabanov, Y., Rásonyi, M., Stricker, C., 2003. On the closedness of sums of convex cones in L⁰$L^0$ and the robust no-arbitrage property. Finance and Stochastics] and by Schachermayer [Schachermayer, W., 2004. The fundamental theorem of asset pricing under poportional transaction costs in finite discrete time. Mathematical Finance 14 (1), 19–48] for markets with proportional transaction costs. More precisely, we restate the notions of consistent and strictly consistent price systems and prove their equivalence to corresponding no arbitrage conditions. We express these results in an analytical form in terms of the subdifferential of the so-called liquidation function. We conclude the paper with a hedging theorem.     

Dualizing optimization problems in mathematical economics

In this paper it is shown how the duality theory of mathematical programming can be applied to many kinds of optimization problems in mathematical economics, even if no objective functions is available, and the usual definition of optimality is replaced by so-called weak optimality. In the latter case only a slight reformulation of the Lagrange problem is required. Two theorems are shown for abstract time-lagged optimization problems over a countably infinite number of periods. The first one is concerned with introducing themultipliers all at once, leading to the consideration of purely finitely additive multipliers, whereas the second one is concerned with introducing them one by one. In general the paper stresses the method of obtaining duality results.     

The relationship between revealed preference and the Slutsky matrix

This paper presents a method of calculating the utility function from a smooth demand function whose Slutsky matrix is negative semi-definite and symmetric. The calculated utility function is the unique upper semi-continuous function corresponding with the demand function. Moreover, we present an axiom for demand functions. We show that under the strong axiom, this new axiom is equivalent to the existence of the corresponding continuous preference relation. If the demand function obeys this axiom, the calculated utility function is also continuous. Further, we show that the mapping from the demand function into a continuous preference relation is continuous, which ensures the applicability of our results for econometrics. Moreover, if this demand function satisfies the rank condition, then our utility function is smooth. Finally, we show that under an additional axiom, the above results hold even if the demand function has corner solutions.     

On the demand generated by a smooth and concavifiable preference ordering

It is shown that if a consumer's preference ordering is strictly convex and is representable by means of a concave, twice continuously differentiable utility function, then the partial derivative of a demanded commodity with respect to its price is bounded from above in a neighborhood of a price vector at which the demand fails to be differentiable. In the case of two commodities, if the demand does not possess finite derivatives with respect to prices at a certain point, then the partial ‘derivative’ of a commodity with respect to its price is equal to minus infinity. The same result holds for n commodities under ‘almost every’ choice of coordinates in the commodity space. If preferences are weakly convex but the same representation assumption holds, demand may not be single-valued but own-price difference quotients are still bounded from above.     

Solvability of perturbation solutions in DSGE models

We prove that the undetermined Taylor series coefficients of local approximations to the policy function of arbitrary order in a wide class of discrete time dynamic stochastic general equilibrium (DSGE) models are solvable by standard DSGE perturbation methods under regularity and saddle point stability assumptions on first order approximations. Extending the approach to nonstationary models, we provide necessary and sufficient conditions for solvability, as well as an example in the neoclassical growth model where solvability fails. Finally, we eliminate the assumption of solvability needed for the local existence theorem of perturbation solutions, complete the proof that the policy function is invariant to first order changes in risk, and attribute the loss of numerical accuracy in progressively higher order terms to the compounding of errors from the first order transition matrix.     

The Solution of Updating or Regionalizing a Matrix with both Positive and Negative Entries

Normally, when updating or regionalizing input-output matrices with negative entries, the negative numbers are first brought outside the matrix, then the matrix is updated or regionalized, then the negative numbers are added back to the result. This is theoretically, and sometimes also empirically, a rather unsatisfactory procedure. This paper proposes a theoretically sound alternative for the presently used ad hoc procedure. Based on the first-order conditions of a restated information loss problem, we generalize the RAS-procedure using reciprocals of the exponential transformations of the related Lagrange multipliers. The diagonal matrices that update or regionalize a given matrix optimally are the solutions of a fixed-point problem. To derive a numerical solution, the paper presents the GRAS-algorithm, which is illustrated in terms of a simple updating example.     

Unfolding intensity function of a Poisson process in models with approximately specified folding operator

Quasi-maximum likelihood histogram sieve estimators of the intensity function of an indirectly observed Poisson process are studied. The setup differs from the standard one in that the exact form of the folding operator may not be known. Instead, approximate knowledge on its discretized version is available. Conditions for strong L ²-consistency are given and admissible discretization rates are studied. In non-folding problems, the number of histogram bins may essentially increase at the usual maximal rate while folding reduces the allowed discretization rates. It is shown that, even in moderately ill-posed problems, the discretization effects may be critical for the strong L ²-convergence and that there is an essential need both for further regularization and for imposing stronger conditions on the estimated function. Not surprisingly, the most restrictive factor is the low approximation power of piecewise constant functions. A regularization method is proposed which suitably modifies the discrete approximation of the folding operator and ensures the strong consistency. Since no penalty term is being introduced, the EM algorithm can be used in its factorized, efficient form. Convergence rates are obtained in terms of the discrete problem. Received: July 1999     

The effects of uncertainty on investment and the expected long-run capital stock

This paper examines the effects of output price uncertainty on the optimal investment behavior of a risk-neutral competitive firm with a constant returns to scale production function. In the presence of convex costs of adjustment, investment is an increasing function of q, the shadow price of capital. Given the current price of output, we find that increased uncertainty will raise the current rate of investment. Increased uncertainty will also increase the expected long-run capital stock if the price of output is serially uncorrelated. However, if the price of output is serially correlated, then the direction of the effect of increased uncertainty on the expected long-run capital stock depends on the curvature of the marginal adjustment cost function. In this case, we obtain results which are directly opposite of the results in the literature and we locate the flaw in the existing analysis.     

General conditions for the existence of maximal elements via the uncovered set

This paper disentangles the topological assumptions of classical results (e.g.,Walker, 1977 on the existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions—with no rationality assumptions on preferences—there is an element such that the upper section of strict preference at that element is minimal in terms of set inclusion, i.e., the uncovered set is nonempty. Assuming the finite subordination property, a condition that weakens known acyclicity and convexity assumptions, each such uncovered alternative is in fact maximal. Implications are a generalization of a result of Yannelis and Prabhakar (1983) on semi-convexity, an extension of Fan’s (1961) lemma on KKM correspondences, and the existence of fixed points for subordinate convex correspondences generalizing the work of Browder (1968).     

Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

Stochastic convex programming: Kuhn-Tucker conditions

Optimality criteria are derived for stochastic programs with convex objective and convex constraints. The problem consists in selecting x₁R^n₁ and so as to satisfy the constraints and minimize total expected cost, where σ is a probability measure. The (basic) Kuhn–Tucker conditions are obtained in terms of conditions on the existence of saddle points of a Lagrangian associated with the stochastic program. We also give an interpretation of these results in terms of equilibrium theory with particular emphasis on a nonstandard price system associated with the restriction that the (first stage) decision x₁ must be chosen independent of the random elements of the problem.     

Scale and scope economies of Japanese private universities revisited with an input distance function approach

This paper examines the scale and scope economies of higher education institutions in Japan assuming the presence of productive inefficiency. The standard approach to testing the scope economies is to apply the cost function. However, the cost function approach often entails the difficulty of obtaining reliable data on input prices, especially the input prices of capital for higher education institutions. This paper proposes a duality approach based on the input distance function. The scope economies are tested under a necessary and sufficient condition by retrieving the costs of joint and separate production from the input distance function. We apply the testing procedure to data pertaining to 218 Japanese private universities in 1999 and 2004. The results indicate the scale economies and the scope diseconomies.     

Asymptotic properties of minimum contrast estimators for parameters of boolean models

Summary This paper presents a method for the estimation of parameters of random closed sets (racs’s) in ℝ ^d based on a single realization within a (large) convex sampling window. The essential idea first applied by Diggle (1981) in a special case consists in defining the estimation by minimizing a suitably defined distance (called contrast function) between the true and the empirical contact distribution function of the racs under consideration, where the most relevant case of Boolean models is discussed in details. The resulting estimates are shown to be strongly consistent (if the racs is ergodic) and asymptotically normal (if the racs is Boolean) when the sampling window expands unboundedly.     

新李嘉图模型:古典定律的当代复兴与拓展构想

新李嘉图模型研究的兴起推动了生产率核心范式重返比较优势问题讨论的视野。然而,当代生产率承载比较优势的新机理,却受到非完全竞争因素和要素禀赋结构异质性及动态化的双重影响。本文一方面探讨开发完全竞争假设改变后新李嘉图模型构造的新古典化处理的技术路径,改进基于产品品种考虑的生产率测度方法;另一方面,鉴于经典的C-D生产函数及其衍生模型难以准确反映开放经济中要素禀赋结构异质性及动态化的现实,借助对Uzawa两部门模型的讨论,建立用来表达要素密集性异质分布和动态变化的影响参数,设定面向经典生产函数的一阶约束条件,首次实现Rybczynski效应的可计算模型化及其同经典生产函数的整合。     

基于治理成本和排污收益的排污权交易定价模型

分别从治理成本和排污收益的角度,构造了排污权交易市场的定价模型。通过凸规划的库恩-塔克条件,求得污染控制区的最佳污染削减方案和最优排污分配方案。拉格朗日乘数u0和λ0具有相同的数值,分别等于排污企业的边际削减成本和边际排污收益,它们可以作为排污权交易市场定价的重要依据。     

一类数量折扣新形式的设计:模糊两级供应链的完美协调

针对市场模糊需求,考虑了由一个供应商和一个销售商组成的两级供应链系统。以供应商为第一视角,构建了一类新的数量折扣形式,并研究了其在分散决策下如何制定数量折扣,使供应链避免"双边际化"效应,实现系统完美协调。基于可信性理论,给出了LR型模糊变量期望值计算式。利用模糊期望利润函数,得到了实现供应链完美协调的条件。数值分析证明了该形式数量折扣的有效性。