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1.
On Fuzzy Portfolio Selection Problems 总被引:1,自引:0,他引:1
The uncertainty of a financial market is traditionally dealt with probabilistic approaches. However, there are many non-probabilistic factors that affect the financial markets. A number of empirical studies showed limitation of using probabilistic approaches in characterizing the uncertainty of the financial markets. Fuzzy set is a powerful tool used to describe an uncertain environment with vagueness, ambiguity or some other type of fuzziness, which are always involved in not only the financial markets but also the behavior of the financial managers' decisions. In a financial optimization model using fuzzy approaches, quantitative analysis, qualitative analysis, the experts' knowledge and the managers' subjective opinions can be better integrated. In this paper, we give an overview on the development of fuzzy portfolio selection to date. Some related problems that might deserve further investigations are also discussed. 相似文献
2.
Ismail Serdar Bakal Joseph Geunes H. Edwin Romeijn 《Journal of Global Optimization》2008,41(4):633-657
In the majority of classical inventory theory literature, demand arises from exogenous sources upon which the firm has little
or no control. In many practical contexts, however, aggregate demand is comprised of individual demands from a number of distinct
customers or markets. This introduces new dimensions to supply chain planning problems involving the selection of markets
or customers to include in the demand portfolio. We present a nonlinear, combinatorial optimization model to address planning
decisions in both deterministic and stochastic settings, where a firm constructs a demand portfolio from a set of potential
markets having price-sensitive demands. We first consider a pricing strategy that dictates a single price throughout all markets
and provide an efficient algorithm for maximizing total profit. We also analyze the model under a market-specific pricing
policy and describe its optimal solution. An extensive computational study characterizes the effects of key system parameters
on the optimal value of expected profit, and provides some interesting insights on how a given market’s characteristics can
affect optimal pricing decisions in other markets. 相似文献
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4.
Discrete approximation, which has been the prevailing scheme in stochastic programming in the past decade, has been extended to distributionally robust optimization (DRO) recently. In this paper, we conduct rigorous quantitative stability
analysis of discrete approximation schemes for DRO, which measures the approximation error in terms of discretization sample size. For the ambiguity set defined
through equality and inequality moment conditions, we quantify the discrepancy between the discretized ambiguity sets and the original set with respect to the Wasserstein metric. To establish the quantitative convergence, we develop a Hoffman error
bound theory with Hoffman constant calculation criteria in a infinite dimensional
space, which can be regarded as a byproduct of independent interest. For the ambiguity set defined by Wasserstein ball and moment conditions combined with Wasserstein ball, we present similar quantitative stability analysis by taking full advantage
of the convex property inherently admitted by Wasserstein metric. Efficient numerical methods for specifically solving discrete approximation DRO problems with
thousands of samples are also designed. In particular, we reformulate different types
of discrete approximation problems into a class of saddle point problems with completely separable structures. The stochastic primal-dual hybrid gradient (PDHG) algorithm where in each iteration we update a random subset of the sampled variables
is then amenable as a solution method for the reformulated saddle point problems.
Some preliminary numerical tests are reported. 相似文献
5.
Mazzeo Rafe 《偏微分方程通讯》2013,38(10):1615-1664
Examples of edge operators include Laplacians on asymptotically flat and asymptotically hyperbolic manifolds. Edge operators also arise in boundary problems around higher condimension boundaries. This paper is concerned with the analysis of general elliptic edge operators with constant indicide roots. We determine when such an operator has a distributional asymptotic expansion. Conditions are given to guarantee that the coefficients of this expansion are smooth. In Part I of this paper we only study the case when the operator is semi-Fredholm. Part II will examine edge operators with infinite dimensional kernel and cokernel, as well as develop the theory of Poisson edge operators. 相似文献
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7.
Daniele Pennesi 《Mathematics and Financial Economics》2018,12(1):55-73
Models with ambiguity averse preferences have the potential to explain some pricing anomalies on financial markets. However, the models used in applications make additional assumptions, beyond ambiguity aversion, on the structure of the investor’s preferences. Therefore, it is not clear how to disentangle the effect of ambiguity aversion from other features of preferences on equilibrium prices. This paper offers a general theory of asset pricing assuming only ambiguity aversion. Price indeterminacy may result in equilibrium when preferences are not smooth. A set of priors, which is identifiable in all the models used in applications, contains the relevant information to price assets. Ambiguity enriches the standard pricing formula by an additional stochastic discount factor and we calculate its explicit form for various models. 相似文献
8.
T. Bermúdez 《Journal of Mathematical Analysis and Applications》2011,373(1):83-93
We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient “computable” criteria for distributional and Li-Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show that every infinite dimensional separable Banach space admits a distributionally chaotic operator which is also hypercyclic. 相似文献
9.
In consumer credit markets lending decisions are usually represented as a set of classification problems. The objective is to predict the likelihood of customers ending up in one of a finite number of states, such as good/bad payer, responder/non-responder and transactor/non-transactor. Decision rules are then applied on the basis of the resulting model estimates. However, this represents a misspecification of the true objectives of commercial lenders, which are better described in terms of continuous financial measures such as bad debt, revenue and profit contribution. In this paper, an empirical study is undertaken to compare predictive models of continuous financial behaviour with binary models of customer default. The results show models of continuous financial behaviour to outperform classification approaches. They also demonstrate that scoring functions developed to specifically optimize profit contribution, using genetic algorithms, outperform scoring functions derived from optimizing more general functions such as sum of squared error. 相似文献
10.
Ghislain R. Franssens 《Mathematical Methods in the Applied Sciences》2013,36(9):1014-1027
The set of associated homogeneous distributions (AHDs) with support in R is an important subset of the tempered distributions because it contains the majority of the (one‐dimensional) distributions typically encountered in physics applications (including the δ distribution). In a previous work of the author, a convolution and multiplication product for AHDs on R was defined and fully investigated. The aim of this paper is to give an easy introduction to these new distributional products. The constructed algebras are internal to Schwartz’ theory of distributions and, when one restricts to AHDs, provide a simple alternative for any of the larger generalized function algebras, currently used in non‐linear models. Our approach belongs to the same class as certain methods of renormalization, used in quantum field theory, and are known in the distributional literature as multi‐valued methods. Products of AHDs on R, based on this definition, are generally multi‐valued only at critical degrees of homogeneity. Unlike other definitions proposed in this class, the multi‐valuedness of our products is canonical in the sense that it involves at most one arbitrary constant. A selection of results of (one‐dimensional) distributional convolution and multiplication products are given, with some of them justifying certain distributional products used in quantum field theory. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
11.
Yi Zhou 《Mathematische Zeitschrift》1999,232(4):707-719
In this paper, we prove that finite energy distributional solutions to the Cauchy problem of wave maps from 1+1 dimensional
Minkowsky space to any complete Riemannian manifold are unique.
Received July 4, 1996; in final form August 25, 1998 相似文献
12.
While estimating parametric production models with risk, one faces two main problems. The first problem is associated with
the choice of functional forms on the mean production function and the risk (variance) function. The second problem is associated
with the specification of the risk preference function. In a parametric model the researcher chooses some ad hoc functional
form on all these. It is obvious that the estimated (i) technology (mean production function), (ii) risk and (iii) risk preference
functions are affected by the choice of functional form. In this paper we consider an estimation framework that avoids assuming
parametric functions on all three. In particular, this paper deals with nonparametric estimation of the technology, risk and
risk preferences of producers when they face uncertainty in production. Uncertainty is modeled in the context of production
theory where producers’ maximize expected utility of anticipated profit. A multi-stage nonparametric estimation procedure
is used to estimate the production function, the output risk function and the risk preference function. No distributional
assumption is made on the random term representing production uncertainty. No functional form is assumed on the underlying
utility function. Rice farming data from Philippines are used for an empirical application of the proposed model. Rice farmers
are, in general, found to be risk averse; labor is risk decreasing while fertilizer, land and materials are risk increasing.
The mean risk premium is about 3% of mean profit. 相似文献
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14.
广义函数Denjoy积分的收敛性问题 总被引:2,自引:0,他引:2
本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续. 相似文献
15.
In this paper, we study a data-driven risk-averse stochastic optimization approach with Wasserstein Metric for the general distribution case. By using the Wasserstein Metric, we can successfully reformulate the risk-averse two-stage stochastic optimization problem with distributional ambiguity to a traditional two-stage robust optimization problem. In addition, we derive the worst-case distribution and perform convergence analysis to show that the risk aversion of the proposed formulation vanishes as the size of historical data grows to infinity. 相似文献
16.
在灰色市场的背景下,构建了由一个制造商和两个独立市场的零售商构成的两阶段供应链模型。依据产品估值将市场分为高端和低端市场,基于价格差异,低端市场的零售商为了实现投机套利会在高端市场中销售原本属于低端市场的产品。研究了灰色市场与制造商广告激励策略对供应链的影响问题。研究表明:若低端市场消费者对产品评价较低,灰色市场可增加制造商的利润;而低端市场消费者对产品估值较高时,灰色市场会减少制造商利润。进一步引入了制造商广告激励策略,得出广告激励不仅可以抑制灰色市场,而且可以在不降低高端市场零售商利润的情况下,让制造商和低端市场零售商的收益增加。 相似文献
17.
Kai He Xi-cheng Zhang 《应用数学学报(英文版)》2007,23(3):501-512
In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion coefficients and distributional drift coefficients. 相似文献
18.
结合我国"军民结合寓军于民"新形势,分析我国军民市场在完全垄断、寡头垄断、垄断竞争三种非完全竞争军品市场中政府和具备军品生产资格的参与企业之间的行为,并利用运筹学和数学规划理论建立了基于企业生产能力的经济优化行为模型,为探讨在军费总额限定条件下政府追求社会产值和企业追求利润最大化提供了新的经济学分析方法. 相似文献
19.
A smoothing method for solving portfolio optimization with CVaR and applications in allocation of generation asset 总被引:2,自引:0,他引:2
This paper focuses on the computation issue of portfolio optimization with scenario-based CVaR. According to the semismoothness of the studied models, a smoothing technology is considered, and a smoothing SQP algorithm then is presented. The global convergence of the algorithm is established. Numerical examples arising from the allocation of generation assets in power markets are done. The computation efficiency between the proposed method and the linear programming (LP) method is compared. Numerical results show that the performance of the new approach is very good. The remarkable characteristic of the new method is threefold. First, the dimension of smoothing models for portfolio optimization with scenario-based CVaR is low and is independent of the number of samples. Second, the smoothing models retain the convexity of original portfolio optimization problems. Third, the complicated smoothing model that maximizes the profit under the CVaR constraint can be reduced to an ordinary optimization model equivalently. All of these show the advantage of the new method to improve the computation efficiency for solving portfolio optimization problems with CVaR measure. 相似文献
20.
Cutting stock problems and bin packing problems are basically the same problems. They differ essentially on the variability of the input items. In the first, we have a set of items, each item with a given multiplicity; in the second, we have simply a list of items (each of which we may assume to have multiplicity 1). Many approximation algorithms have been designed for packing problems; a natural question is whether some of these algorithms can be extended to cutting stock problems. We define the notion of “well-behaved” algorithms and show that well-behaved approximation algorithms for one, two and higher dimensional bin packing problems can be translated to approximation algorithms for cutting stock problems with the same approximation ratios. 相似文献