Comparisons on aggregate risks from two sets of heterogeneous portfolios

In this paper, we stochastically compare the aggregate risks from two heterogeneous portfolios. It is shown that under suitable conditions the more heterogeneities among aggregate risks would result in larger aggregate risks in the sense of the stochastic order. The stochastic properties of aggregate risks when the claims follow proportional hazard rates models or scale models are studied. We also provide sufficient conditions for comparing the aggregate risks arising from two sets of heterogeneous portfolios with claims having gamma distributions. In particular, the aggregate risks of portfolios from dependent samples with comonotonic dependence structures or arrangement increasing density functions are discussed. The new results established strengthen and generalize several results known in the literature including Ma (2000), Khaledi and Ahmadi (2008), Xu and Hu (2011), Xu and Balakrishnan (2011), Pan et al. (2013) and Barmalzan et al. (2015).     

Valuation of intergenerational transfers in funded collective pension schemes

This paper applies contingent claim analysis to value pension contracts for real-life collective pension plans with intergenerational risk sharing and offering DB-like benefits. We rewrite the balance sheet of such a pension fund as an aggregate of embedded generational options. This implies that a pension fund is a zero-sum game in value terms, so any policy change inevitably leads to value transfers between generations. We explore intergenerational value transfers that may arise from a plan redesign or from changes in funding policy and risk sharing rules. We develop a stochastic framework which accounts for time-varying investment opportunities and computes the embedded generational options. Changes in the values of the generational options enable us to evaluate the impact of policy modifications in the pension contract with respect to intergenerational transfers and redistribution. We find that a switch to a less risky asset mix is beneficial to elderly members at the expense of younger members who lose value. A reallocation of risk bearing from a plan with flexible contributions and fixed benefits to a plan with fixed contributions and flexible benefits leads to value redistribution from older plan members to younger ones.     

Hierarchical Production-planning Systems: Extensions and Modifications

This paper extends earlier hierarchical production-planning approaches initiated by Hax and Meal. The proposed model incorporates both functional and hierarchical interfaces simultaneously as encountered in practice, and assures feasibility and consistency among the decisions made at the different hierarchical levels of the firm. The problem of infeasibility which arises in disaggregating the aggregate production plan into detailed schedules is solved using goal programming at the product-family disaggregation level, and using branch and bound at the item-disaggregation level. The proposed approach minimizes backlogging regardless of the underlying cost structure of the problem at hand.     

On optimal search plans to detect a target moving randomly on the real line

A target, whose initial position is unknown, is performing a random walk on the integers. A searcher, starting at the origin, wants to follow a search plan for which E[τ^k] is finite, where k ≥ 1 and τ is the time to capture. The searcher, who has a prior distribution over the target's initial position, can move only to adjacent positions, and cannot travel faster than the target. Necessary and sufficient conditions are given for the existence of search plans for which E[τ^k] is finite and a minimum.     

A smoothing Newton method for mathematical programs governed by second-order cone constrained generalized equations

In this paper, we consider a class of mathematical programs governed by second-order cone constrained parameterized generalized equations. We reformulate the necessary optimality conditions as a system of nonsmooth equations under linear independence constraint qualification and the strict complementarity condition. A set of second order sufficient conditions is proposed, which is proved to be sufficient for the second order growth of the stationary point. The smoothing Newton method in [40] is employed to solve the system of nonsmooth equations whose strongly BD-regularity at a solution point is demonstrated under the second order sufficient conditions. Several illustrative examples are provided and discussed.     

Nash equilibrium in a pay-as-bid electricity market: Part 1 – existence and characterization

We consider a model of a pay-as-bid electricity market based on a multi-leader-common-follower approach where the producers as leaders are at the upper level and the regulator as a common follower is at the lower level. We fully characterize Nash equilibria for this model by describing necessary and sufficient conditions for their existence as well as providing explicit formulas of such equilibria in the market.     

A Hospital Throughput Model in the Context of Long Waiting Lists

In a public health system, one of the problems is the size of the waiting list for admission to hospital. This research involves establishing a method of analysing the general surgery waiting list problem at hospital and district level. While there are many aspects to such a study, this paper concentrates on a linear programming model to plan the aggregate throughput of the general surgical department. Preliminary results from applying the techniques to actual health districts in the United Kingdom are reported.     

Improving PRETREE's predictive capabilities

Compared to compensatory type choice models (e.g., logit), hierarchical choice models have been used much less frequently in the real world. This has happened even though there is a lot of evidence to suggest that the hierarchical structure is closer to the actual process by which individuals make choices. In this paper, we have considered one of the original hierarchical models (PRETREE). The PRETREE model has been heavily cited in the marketing and psychometric literatures. We wish to examine PRETREE at the aggregate level making n-way (market share) predictions.A primary strength of the PRETREE model was its apparent ability to capture violations of the property of the “independence of irrelevant alternatives” (IIA). We prove that there are limitations to this argument. We suggest a method to overcome these limitations; this change resulted in substantial improvement in the predictive abilities of the model, when the modified PRETREE is applied to real world data. The predictions are at an aggregate level on a hold-out sample.The above modification to PRETREE will hopefully not only renew but also increase interest in applying a hierarchical approach to modeling real-world problems on choice.     

Collective adjustment of pension rights in ALM models

Collective adjustment of pension rights is a way to keep defined benefit systems tenable. In asset liability management (ALM) models presented in the literature these decisions are modeled both at the aggregate level of the liabilities as a whole and at a more detailed level. In this paper we compare the approximate aggregate approach to the accurate detailed approach for the average earnings scheme with conditional indexation. We prove that the aggregate approach leads to one-sided errors. Moreover, we show that for semi-realistic data these biases are considerable.     

NONVANISHING OF CONFORMAL BLOCKS DIVISORS ON $$ {\overline{\mathrm{M}}}_{0,n} $$

We introduce and study the problem of finding necessary and sufficient conditions under which a conformal blocks divisor on \( {\overline{\mathrm{M}}}_{0,n} \) is nonzero, solving the problem completely for \( \mathfrak{s}{\mathfrak{l}}_2 \). We give necessary nonvanishing conditions in type A, which are sufficient when theta and critical levels coincide. We also show divisors are subject to additive identities, reflecting a decomposition of the weights and level.     

Cyclic BSEC of block size 3

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this note, we discuss constructions of these designs having cyclic automorphisms. We use Langford sequences to construct all possible cyclic BSEC (or CBSEC) with block size 3 and λ = 1,2, which establishes the necessary and sufficient conditions for such designs. Some constructions of the balanced sampling plan avoiding adjacent units, a generalization of BSEC, are also given for fixed λ.     

Aggregate–disaggregate approach to an airfreight forwarder’s planning under uncertainty: a case study

Resource planning of airfreight forwarders is a complex endeavor, requiring decisions to be made in a dynamic and uncertain environment. Airfreight forwarders acquire airfreight spaces from three sources: allotment from carriers, retail from carriers and subcontracting to partners, all of which differ in terms of cost, flexibility and timing of booking. This real-life problem has many planning decisions (bookings in terms of carriers, route, time, ULDs, etc.). In this case study, we propose an aggregate–disaggregate approach and focus on the most critical decisions. A two-stage stochastic dynamic program first determines, in aggregates, the amount of allotment bookings, retail resources, and subcontracting or surplus co-loading. Then, a heuristic is used to disaggregate resource requirements into specific bookings. An analysis is provided to examine the relevant managerial issues. Based on real-life data, we show several patterns of aggregate resource bookings with respect to different levels of demand uncertainty and cost parameters. We show that resource disaggregation has to balance cost-effectiveness, capacity flexibility and routing flexibility of a resource plan.     

The Optimality of the ‘Zero-Switch’ Rule for a Class of Economic Lot-Scheduling Problems

The economic lot-scheduling problem for the single-machine, n-item scheduling problem has received attention in a number of journals. One approach is to define a sequence (called the fundamental cycle) in which every item is made at least once, and then to determine the length of production runs consistent with the aggregate inventory level which will maximize the length of the cycle duration. The assumption that production is switched from one item to the next only when the inventory level of the latter reaches zero is often used in heuristic solutions to these models. This paper illustrates the conditions in which the ‘zero-switch’ rule is a necessary condition at the optimal solution for situations in which demand is continuous and production capacity equals aggregate demand.     

An approach for an algorithmic solution of discrete optimal control problems and their game-theoretical extension

We consider time discrete systems which are described by a system of difference equations. The related discrete optimal control problems are introduced. Additionally, a gametheoretic extension is derived, which leads to general multicriteria decision problems. The characterization of their optimal behavior is studied. Given starting and final states define the decision process; applying dynamic programming techniques suitable optimal solutions can be gained. We generalize that approach to a special gametheoretic decision procedure on networks. We characterize Nash equilibria and present sufficient conditions for their existence. A constructive algorithm is derived. The sufficient conditions are exploited to get the algorithmic solution. Its complexity analysis is presented and at the end we conclude with an extension to the complementary case of Pareto optima.Dmitrii Lozovanu was Supported by BGP CRDF-MRDA MOM2-3049-CS-03.     

Ideaux de polynomes et ideaux de valeurs

Let B be the ring of integral valued polynomials over a noetherian domain A. We study in which case finitely generated ideals of B are uniquely determined by their ideals of values at each element of A. We give necessary and sufficient conditions which are verified for example when A is any ring of integers of an algebraic number field, such that each quotient ring Am with respect to a maximal ideal m is analytically irreducible.     

Preprocessing techniques and column generation algorithms for stochastically efficient demand

We construct a discrete-time, multi-period replenishment plan that integrates the inventory, production and distribution functions and that satisfies the conditions of a very demanding cycle service level. The corresponding optimization problem takes the form of a very complex mixed-integer stochastic program. We develop a new enumerative algorithm that identifies the stochastically efficient demand trajectories at an authorized level of stockout, and derive three algorithmic preprocessing techniques used to discriminate the above trajectories. The application of the enumerative and preprocessing algorithmic approaches transforms the stochastic program into a disjunctive integer program solved through a column generation that reduces the risk of a bottleneck in the distribution resources of the supply chain. Computational results evaluate the efficiency of the algorithmic developments proposed in this paper, and attest the quality and robustness of the solution method. The solution methodology is validated on a real-life problem.     

Dynamic Network Inventory Control Model with Interval Nonstationary Demand Uncertainty

We consider a dynamic inventory control system described by a network model with an interval assigned nonstationary demand. We assume that unknown demand may take any value within the interval, which bounds depend on time. In terms of Kaucher interval arithmetic, we derive necessary and sufficient conditions for the existence of a feasible feedback control and sufficient conditions for the existence of an optimal feedback control strategy. We obtain an optimal feasible storage level and estimate the rate of the system convergence to this level. Then we develop the algorithm of finding the optimal control strategy. These results are applied to an example.     

On Quillen?s Theorem A for posets

A theorem of McCord of 1966 and Quillen?s Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We give an alternative elementary proof of this result and we deduce also a stronger statement: under the hypotheses of the theorem, the map is not only a homotopy equivalence but a simple homotopy equivalence. This leads then to stronger formulations of the simplicial version of Quillen?s Theorem A, the Nerve Lemma and other known results. In particular we establish a conjecture of Kozlov on the simple homotopy type of the crosscut complex and we improve a well-known result of Cohen on contractible mappings.