Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims—an underlying frictionless linear pricing rule—that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches—a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule—the supremum of the underlying frictionless linear pricing rules—for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.     

一致凸的L~p空间在不动点问题中的应用

本文运用一致凸的Banach空间理论,讨论了Lp空间有界区域的极小半径问题和正交变换群作用的不动点问题,获得L(pΩ)空间的非空有界集一定存在唯一点x0∈Lp(Ω),使得f(x0)=x∈Lp(Ω)inf f(x),利用此结论还得到正交变换群作用在L(pB)空间上存在不动点。     

Insurance contracts portfolios with heterogenous parametric life distributions

In this paper we consider two portfolios: one of m endowment insurance contracts and one of m whole life insurance contracts. We introduce the majorization order, Schur functions, and parametric families of distribution functions. We assume that the owners of the portfolios are exposed to different members of a known parametric family of distributions and study the effect of this stochastic heterogeneity on the premiums and death benefits of the insurance contracts. We show that the premiums paid in both contracts are Schur concave and that the death benefit awarded in the whole life contract is Schur convex. We provide upper and lower bounds for the premiums and for the death benefit, and compute the bounds for four parametric families of distribution functions used frequently in the Actuarial Sciences.     

关于凸函数的连续性的一些结果

凸函数是数学分析中的一类重要函数,而函数的连续性又是函数性态的一项基本而又重要的特征.文章从凸函数的定义出发,讨论了凸函数与连续的关系,得出了连续函数不一定是凸函数,凸函数也不一定连续的结论,给出了判别连续凸函数的几个充要条件及连续凸函数的几条特殊性质.     

集值映射几种广义凸性之间关系

集值映射向量优化问题是最优化理论中的一个重要方向.文[1]中提出了集值映射的一种新的广义凸性:生成锥内部-锥-类凸(简记为ic-锥-类凸),并研究了这种广义凸性在集值向量优化问题中的一些应用。本文在序锥内部非空和序锥内部为空集的条件下,给出了这种广义凸性和其他几种广义凸性之间的关系。     

The equivalence of the bishop-de leeuw and the pigou dalton order structures of measures

In this paper it is shown that the Bishop-de Leeuw and the Pigou-Dalton order structures of measures are the same.

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Riassunto In questo lavoro viene dimostrato, che le structture d’ordine per le misure di Bishop-de Leeuw e di Pigou-Dalton si equivalgono.

     

紧算子空间K(l_P,Z)(1

卜庆营 《河北工业科技》1993,(2)

Isotonic estimators of monotone densities and distribution functions: basic facts

We present short proofs of some basic results from isotonic regression theory. A straightforward argument is given to show that the left continuous version of the concave majorant of the empirical distribution function maximizes the likelihood function f↦f (X,)… f (X _n ) within the class of non-increasing densities. Similarly, it is shown that the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of interval censored data has an interpretation in terms of the left derivative of a convex minor ant. Finally, a short proof is given to show that the number of vertices of the concave major ant of the uniform empirical distribution function is asymptotically normal with asymptotic mean and variance both equal to log n .     

Quantile-locating functions and the distance between the mean and quantiles

Given a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p -quantile of X and its mean in terms of the central absolute first moment of X . The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.