Pro Rata Allocation Research Articles

The inoculation dilemma: Partial vs Full immunization during the early rollout in a pandemic

COVID-19 demonstrated the extent to which a pandemic can affect billions of lives worldwide. Vaccinations are an effective intervention that reduces the burden of the disease on the population. However, the low availability of vaccine doses coupled with an emerging infection wave calls for efficient dose allocation. We study the tradeoffs between prioritization of partial or full immunization while allocating limited doses with the help of an augmented SIR model. We define the term allocation ratio as the ratio of doses allocated for partial immunization as a proportion of the total available doses. Optimal control theory is used to derive the path traversed by the allocation ratio throughout the vaccine administration program. Numerical insights are obtained by introducing the case study of the Indian state of Tamil Nadu. Results indicate a preference towards full immunization when the active infections are low, while a switch to exclusive partial immunization is observed as the infection wave grows. Sensitivity analysis shows that factors like reduced vaccine availability, higher transmission rate, and high first-dose efficacy promote a quicker switch. The results also indicate significant potential savings of around ₹710 billion (∼ $8.46 billion) in mortality losses compared to the more widely followed pro-rata allocation policies. Hence, our study contributes to the growing discussion around the optimal strategy for vaccine administration with a focus on dose prioritization. The results of our research can help policymakers determine the allocation of limited available doses when faced with rising infection numbers during future pandemics.

Optimal spatial evaluation of a pro rata vaccine distribution rule for COVID-19

The COVID-19 Vaccines Global Access (COVAX) is a World Health Organization (WHO) initiative that aims for an equitable access of COVID-19 vaccines. Despite potential heterogeneous infection levels across a country, countries receiving allotments of vaccines may follow WHO’s allocation guidelines and distribute vaccines based on a jurisdictions’ relative population size. Utilizing economic—epidemiological modeling, we benchmark the performance of this pro rata allocation rule by comparing it to an optimal one that minimizes the economic damages and expenditures over time, including a penalty representing the social costs of deviating from the pro rata strategy. The pro rata rule performs better when the duration of naturally- and vaccine-acquired immunity is short, when there is population mixing, when the supply of vaccine is high, and when there is minimal heterogeneity in demographics. Despite behavioral and epidemiological uncertainty diminishing the performance of the optimal allocation, it generally outperforms the pro rata vaccine distribution rule.

Comparative performance of between-population vaccine allocation strategies with applications for emerging pandemics

Vaccine allocation decisions during emerging pandemics have proven to be challenging due to competing ethical, practical, and political considerations. Complicating decision making, policy makers need to consider vaccine allocation strategies that balance needs both within and between populations. When vaccine stockpiles are limited, doses should be allocated in locations to maximize their impact. Using a susceptible-exposed-infectious-recovered (SEIR) model we examine optimal vaccine allocation decisions across two populations considering the impact of characteristics of the population (e.g., size, underlying immunity, heterogeneous risk structure, interaction), vaccine (e.g., vaccine efficacy), pathogen (e.g., transmissibility), and delivery (e.g., varying speed and timing of rollout). Across a wide range of characteristics considered, we find that vaccine allocation proportional to population size (i.e., pro-rata allocation) performs either better or comparably to nonproportional allocation strategies in minimizing the cumulative number of infections. These results may argue in favor of sharing of vaccines between locations in the context of an epidemic caused by an emerging pathogen, where many epidemiologic characteristics may not be known.

Optimizing Spatio-Temporal Allocation of the COVID-19 Vaccine Under Different Epidemiological Landscapes.

An efficient and safe vaccine is expected to allow people to return to normal life as soon as possible. However, vaccines for new diseases are likely to be in short supply during the initial deployment due to narrow production capacity and logistics. There is an urgent need to optimize the allocation of limited vaccines to improve the population effectiveness of vaccination. Existing studies mostly address a single epidemiological landscape. The robustness of the effectiveness of other proposed strategies is difficult to guarantee under other landscapes. In this study, a novel vaccination allocation model based on spatio-temporal heterogeneity of epidemiological landscapes is proposed. This model was combined with optimization algorithms to determine the near-optimal spatio-temporal allocation for vaccines with different effectiveness and coverage. We fully simulated the epidemiological landscapes during vaccination, and then minimized objective functions independently under various epidemiological landscapes and degrees of viral transmission. We find that if all subregions are in the middle or late stages of the pandemic, the difference between the effectiveness of the near-optimal and pro-rata strategies is very small in most cases. In contrast, under other epidemiological landscapes, when minimizing deaths, the optimizer tends to allocate the remaining doses to sub-regions with relatively higher risk and expected coverage after covering the elderly. While to minimize symptomatic infections, allocating vaccines first to the higher-risk sub-regions is near-optimal. This means that the pro-rata allocation is a good option when the subregions are all in the middle to late stages of the pandemic. Moreover, we suggest that if all subregions are in the period of rapid virus transmission, vaccines should be administered to older adults in all subregions simultaneously, while when the epidemiological dynamics of the subregions are significantly different, priority can be given to older adults in subregions that are still in the early stages of the pandemic. After covering the elderly in the region, high-risk sub-regions can be prioritized.

CROSS-BORDER GROUP INSOLVENCY, A STUDY OF NORTEL CASE

Introduction. This Article is a detailed analysis of one of the most complex and landmark judgments in the area of cross border group insolvency. It traces the timeline of the insolvency of Nortel Plc. and the simultaneous proceedings in multiple jurisdictions. Introduction followed by Literature Review. Research methods are exploratory in nature, since the study has to explore a case of the simultaneous proceedings in multiple jurisdictions. Results and discussions. The Article discusses that there are two major methods for dealing with corporate groups undergoing insolvency, which are: Procedural Coordination and Substantive Consolidation. Under such mechanisms which little to no precedence in any jurisdiction, this case carved out its own path to arrive at the outcome of Pro-Rata Allocation. The case is significant for being heard at the same time in two courtrooms, one in Delaware and one in Ontario, that were linked in order to receive live evidence together. This Article discusses the importance and significance of having a cross border group insolvency regime in place. In the era of Globalisation, the integration of national economies into a global economic system has been one of the most important developments of the last century

SIZE PRECEDENCE AND SHARE VOLUME: THE CASE OF THE PSX EXCHANGE

Most equity exchanges operate with a price-time priority market structure. Using a natural experiment, this study examines the ability of an exchange to attract share volume when size is the secondary precedence rule. In 2010, the NASDAQ OMX Group, Inc. and the Philadelphia Exchange launched the PSX equity exchange with a price-size pro-rata allocation market model. When operating under a pro-rata allocation algorithm, PSX is able to attract more volume than during a price-time regime. Systemic factors are imperative, as there is substantial evidence that the PSX attracts volume in times of heightened market volatility, but PSX volume decreases when market returns are positive. Competition is increasingly important in a fragmented market. There is evidence that order routing fees and the prevalence of off-exchange trading are significant factors in the ability of the PSX to capture market share. The results are of interest to market participants, regulators, and exchange officials.

Exchange Fees and Overall Trading Costs

In the US market, two popular exchange fee structures are “maker-taker” and “inverted” (also known as “taker-maker”). Maker-taker exchanges charge fees for taking liquidity and give rebates for providing liquidity, while inverted exchanges give rebates for taking liquidity and charge fees for providing liquidity. Using live trade data from an institutional investor that applies a flexible trading approach and seeks to participate in the natural market liquidity, we find that net of fees and rebates, trading costs are statistically indistinguishable between maker-taker and inverted exchanges. This finding has important implications for venue routing decisions in trading algorithms that do not demand immediacy, suggesting that the optimal routing strategy in terms of the tradeoff between cost and volume per unit of time is a pro-rata allocation across venues. It is also relevant to the recent discussions on legislation to fix fees across all trading venues.

Optimizing spatial allocation of seasonal influenza vaccine under temporal constraints.

Prophylactic interventions such as vaccine allocation are some of the most effective public health policy planning tools. The supply of vaccines, however, is limited and an important challenge is to optimally allocate the vaccines to minimize epidemic impact. This resource allocation question (which we refer to as VaccIntDesign) has multiple dimensions: when, where, to whom, etc. Most of the existing literature in this topic deals with the latter (to whom), proposing policies that prioritize individuals by age and disease risk. However, since seasonal influenza spread has a typical spatial trend, and due to the temporal constraints enforced by the availability schedule, the when and where problems become equally, if not more, relevant. In this paper, we study the VaccIntDesign problem in the context of seasonal influenza spread in the United States. We develop a national scale metapopulation model for influenza that integrates both short and long distance human mobility, along with realistic data on vaccine uptake. We also design GreedyAlloc, a greedy algorithm for allocating the vaccine supply at the state level under temporal constraints and show that such a strategy improves over the current baseline of pro-rata allocation, and the improvement is more pronounced for higher vaccine efficacy and moderate flu season intensity. Further, the resulting strategy resembles a ring vaccination applied spatiallyacross the US.

Auction design for gas pipeline transportation capacity—The case of Nabucco and its open season

As a response to the Russian dominance of the EU's natural gas supplies and the EU's increasing gas demands, major gas pipeline projects are currently under way to enhance the EU's energy supply security. Oftentimes to raise financing and to allocate gas transportation capacities, auctions are carried out to allow gas shippers to book transportation rights. In recent years, auctions have emerged as one of the most successful allocation mechanisms in the microeconomic theory. However, different auction designs can lead to different outcomes making the choice of auction design a decisive one, especially for divisible-good auctions. This paper seeks to give a formulation of an optimal auction design for gas pipeline transportation capacity. Specifically three different mechanisms are tested: (i) NPV allocation; (ii) pro rata allocation; and (iii) optimization. In addition, Nabucco is taken as a case study to empirically show results of such auction designs. Results show that a trade-off between revenue optimization and fair allocation can be observed: allocation per optimization is the favorable auction design when revenue maximization is more important than fair allocation. On the other hand, pro rata allocation is the auction design to be chosen when fairness of allocation is considered most central.

Group Bargaining and Conflict

We consider a situation where groups negotiate over the allocation of a surplus (which is used to fund group specific goods). Each group is composed of agents who have differing valuations for public goods. Members choose a representative to take decisions on their behalf. Specifically, representatives can decide to enter either a (cooperative) negotiation protocol or a conflict to appropriate the surplus. In the cooperative negotiations, disagreement corresponds to a pro rata allocation (as a function of the size of the groups). We analyse the conditions (on the internal composition of the groups) under which conflict will be preferred to negotiated agreements (and vice versa), and we derive welfare implications. Finally, we provide results of comparative statics that highlight the influence of changes in the internal composition of groups and in their relative size on the profitability of negotiated agreements.

Spatial considerations for the allocation of pre-pandemic influenza vaccination in the United States

The impact of the next influenza pandemic may be mitigated by inducing immunity in individuals prior to the start of national epidemics using a pre-pandemic vaccine targeted against current avian influenza strains. The US Department of Health and Human Services (HHS) intends that pre-pandemic vaccines will be allocated to states in proportion to the size of their population in predefined priority groups, i.e. approximately pro-rata. We show that such an equitable policy is likely to be the least efficient in terms of the number of infections averted. We demonstrate that the potential benefits could be substantial if a fully discretionary policy is allowed, i.e. if some regions are allocated sufficient vaccines to achieve herd immunity while other regions are allocated no vaccine. Since such an inequitable policy may be impractical, we consider the sensitivity of an intermediate policy (in which 50% of the stockpile is allocated on a pro-rata basis) to key transmission uncertainties. The benefits of the 50% discretionary policy are sensitive to parameter values which cannot be known in advance. Therefore, despite substantial potential benefits of non-pro-rata policies, our results suggest that the current HHS policy of pro-rata allocation by state is a good compromise in terms of simplicity, robustness, equity and efficiency.

Reviewing Allocation Law in The Wake of Con Edison

INTRODUCTION Generally, there are two approaches to allocating long-term toxic tort claims like asbestos or environmental contamination. One is the “prorata” allocation method, whereby each party, including policyholders in certain circumstances, is held responsible only for its “fair share” of the liability. Courts who adopt this position rely on the policy language that states that the insurer will only cover bodily injury or property damage taking place during the policy period. The difficulty lies in determining how to calculate the “fair share.” Courts have approached the calculation issue in different ways, such as straight time on the risk, time on the risk in relation to limits, or horizontal exhaustion before any excess carrier pays. However, pro rata allocation is not favorable to policyholders because it usually places responsibility on them for periods of insurance gaps, whether by reason of missing policies, insolvencies, self-insured retentions/deductibles, or periods of no insurance. The second method is known as “joint and several liability” or “pick and choose”. This method is more favorable to policyholders because it places the burden of allocating “fair share” responsibility for the claim on the insurers. Specifically, pick and choose allows the policyholder to select the policy (and sometimes policies) that will respond to a tendered claim. Notwithstanding that the loss takes place over a long period of time, under a pick and choose method of allocation, the insurer issuing the selected policy becomes responsible to pay for the policyholder’s entire liability up to its policy limit. Thereafter, that insurer is entitled to seek contribution from any other insurer that may have responsibility for the loss, but not from the insured.

An Empirical Analysis of Price and Time Priority and Pro Rata Trade Execution Algorithms in Screen-Traded Markets

One of the biggest issues in futures markets today is the introduction and proliferation of all-electronic exchanges and the procedures they will adopt for trading. This article looks at the impact of a 1998 change in trading procedures for Eurodollar futures on the Globex2 system used for after-hours trading by the Chicago Mercantile Exchange. The original system, which maintained price and time priority for limit orders on the book, was replaced by one with pro rata allocation for all orders at the same price, regardless of time arrival. The existence of the regular hours open outcry system operating without change during the same time period provides a control sample against which the behavior of Globex2 prices in the two different regimes can be compared. The results suggests that the change in the trading algorithm had no significant effect on the bid-ask spread or on the volatility in this market.

A finite difference type algorithm with pro rata resource allocation

We describe an algorithm that uses pro rata allocation between inter-pool flows to meet conservation of mass/energy constraints and avoid execution order dependence. More commonly used clipping methods do not satisfy these constraints when multiple flows from small pools exceed the total size of the pool. Overrun, which occurs when a pool is increased or decreased beyond its capacity, typically a decrease below zero, leads to failure to conserve mass. Clipping avoids overrun by restricting the size of pools, usually by setting negative values to zero, which can in turn lead to unacceptable error levels in the simulation's output, particularly in terms of sensitivity to execution order. In addition to the normal ‘current’ and ‘next’ copies of the system's state variables, this algorithm requires an ‘output’ copy, which sums outputs from each pool. Individual flows from a pool are divided by the output sum to determine the proportion of the pool each flow receives. Additionally, the approach allows tracking of individual mass flows, which are sometimes more interesting than their net effect on the pools on which they operate. Implementation details and a comparison with a clipping type algorithm are given in terms of a GIS based meadow ecosystem hydrology submodel. In a simple test case, also presented, the pro rata algorithm more consistently tracks the target solution (given by an extremely small time step).