Multi-period Setting Research Articles

A Dynamic Model of Lawsuit Joinder and Settlement

In this paper we examine a dynamic model of the process by which multiple related lawsuits may be filed and combined; we also examine actions a defendant may employ that may disrupt the formation of a joint suit. Our initial model involves two potential plaintiffs, with private information about the harm they have suffered, in a multi-period setting with positive costs of filing a suit. If two plaintiffs file, they join their suits to obtain a lower per-plaintiff trial cost and a higher likelihood of prevailing against the defendant. We find that some plaintiff types never file, some wait to see if another victim files and only then file, some file early and then drop their suits if not joined by another victim and, finally, some file and pursue their suits whether or not they are joined; thus, the equilibrium resembles a 'bandwagon.'We then consider the effect of allowing preemptive settlement offers by the defendant aimed at discouraging follow-on suits. Preemptive settlement results in a 'gold rush' of cases into the first period. In general, plaintiffs (ex ante) strictly prefer that such preemptive settlements not be allowed, and computational results suggest this may be broadly true for defendants as well; however, the inability of defendants to commit to such a policy results in an equilibrium with preemptive settlement. Finally, we consider partial unawareness of victims as to the source of harm; this provides a role for plaintiffs’ attorneys, who may seek additional victims to join a combined lawsuit. Confidential preemptive settlements in the case of partial unawareness restrict the plaintiff’s attorney from seeking additional victims and therefore leads to higher preemptive settlement amounts. Moreover, the defendant strictly prefers to employ preemptive settlement if the fraction of unaware victims is sufficiently high.

Formas de Financiamento das Empresas: Um Modelo Teórico

O objetivo deste artigo é fornecer subsídios para a compreensão de em quais circunstâncias a utilização de um intermediário financeiro é preferido à utilização de um mercado de capitais descentralizado, bem como entender as razões pelas quais os dois tipos de financiamento (direto e intermediado) coexistem. Para tanto, será desenvolvido um modelo no qual um contexto em que a existência de efeitos de free-rider (carona) leva à criação de oportunidades de ganhos para um intermediário financeiro, existindo informação assimétrica entre credores e devedores. Em um passo seguinte, este modelo será ampliado, fazendo com que a análise se desenrole por mais de um período de tempo. Neste ponto, buscamos compreender se, em um contexto de interação repetida entre os agentes, a disponibilidade de informações sobre o histórico de pagamentos de um devedor alteraria os resultados anteriormente obtidos.

Measurement of income mobility: a re-examination

This paper reviews different characterizations of income mobility, trying to establish links between them and showing that some of them are equivalent. Furthermore, exploiting recent advances in multidimensional inequality measurement, we generalize mobility measurement from the two-period to the multi-period setting, come up with new ways to decompose total mobility into exchange as opposed to structural mobility, and introduce new indices of mobility with desirable properties.

The Impact of R&D Tax Incentives on R&D Costs and Income Tax Burden

We analyse R&D tax incentives in a detailed way considering a multi-period setting and economic assumptions which reflect a realistic economic environment. We measure the incentive's impact on the firm's total tax payments and the R&D cost by means of the simulation model European Tax Analyzer. Using different economic settings and model firms, we run sensitivity analyses and get by that a more detailed view on the effects from R&D tax incentives against the background of the framing tax system. We find that not so much the kind but rather the specific design of R&D tax incentives, the interplay with the framing tax system and the firm's profitability relative to the level of R&D expenditures heavily influence the amount of tax subsidy for R&D.

Neuroaccounting, Part II: Consilience Between Accounting Principles and the Primate Brain

We develop the hypothesis that culturally evolved accounting principles are ultimately explained by their consilience with how the human brain has biologically evolved to evaluate opportunities for exchange. The primary function of accounting in evaluating exchange is providing information on the net benefits of past exchanges. Accounting's comparative advantage arises because it provides information based on reliable quantified data that is well suited to multi-period settings where reputation and trust are of first-order importance. We review evidence documented by neuroscientists that is consistent with the hypothesis that longstanding accounting principles such as Revenue Realization, Expense Matching, Objectivity, Historical Cost, Going Concern and Conservatism have distinct parallels in brain behaviors. We conclude that NeuroAccounting has important implications for how we think about accounting principles and the ultimate forces behind their emergence and persistence.

An efficient ex-ante criterion for ranking investment strategies

Fisher separation theorem [T.E. Copeland, J.F. Weston, K. Shastri, Financial Theory and Corporate Policy, fourth ed., Addison Wesley, New York, 2005] states that, in a perfect and complete capital market, the investment decisions of a firm are to maximize the wealth of its current shareholders regardless of their preferences. In this study, we integrate Dybvig’s [P.H. Dybvig, Inefficient dynamic portfolio strategies or how to throw away a million dollars in the stock market, Review of Financial Studies 1 (1988) 67–88; P.H. Dybvig, Distributional analysis of portfolio choice, Journal of Business 61 (1988) 369–393] payoff distribution pricing model (PDPM) into the framework of this separation theorem and propose that an investment firm with numerous shareholders can use the inefficiency amount of the PDPM as a decision criterion for ranking ex-ante investment strategies in order of their value to the firm. For implementation, we formulate the PDPM in a multiperiod setting and develop an operational formula for computing the inefficiency amount of any strategy. Finally, using simulation, we compare four commonly used fixed-income strategies based on their inefficiency amounts.

Mini-Workshop: Mathematics of Solvency

The mini-workshop Mathematics of Solvency , organised by Freddy Delbaen (Zurich), Karl-Theodor Eisele (Strasbourg) and Christian Hipp (Karlsruhe) was held during the week February 10th–February 16th, 2008. The 15 participants from academia and practice – most of whom came from supervision authorities – discussed the foundation of mathematical concepts for risk and risk measurement as well as their consequences for various decision or control activities in financial services. Such concepts are of major importance for the definition of a necessary solvency capital – which takes into account diversification effects – for banks, investors, and insurers, from the perspective of supervision, of risk management, of rating, and of capital allocation. They help industry to develop consistent foundations for dealing with insurance and financial risks. The investigation of risk concepts in the multi period setting leads to new mathematical questions in the theory of stochastic processes. A sensible definition of a risk measure requires the property of super-additivity with respect to different risks as well as a submartingale property with respect to time. Such a definition leads to a theory of non-linear pricing of risks, as well as to a better understanding of the time evolution of risk assessment. These two concepts were not treated in traditional finance. The consistency of risk measurement over different time intervals leads to monotonicity properties of convex functionals. The representation of these time consistent valuations is related to backward stochastic differential equations and difference equations, respectively. The information available to agents is modeled with filtrations and the difference in information leads to problems known as enlargement of filtrations. In the talks, methods and concepts from various fields were used: stochastic processes, game theory, functional analysis, and stochastic control. In addition, experience with existing and operating real world risk valuation concepts has been reported and discussed.

A selective newsvendor approach to order management

AbstractConsider a supplier offering a product to several potential demand sources, each with a unique revenue, size, and probability that it will materialize. Given a long procurement lead time, the supplier must choose the orders to pursue and the total quantity to procure prior to the selling season. We model this as a selective newsvendor problem of maximizing profits where the total (random) demand is given by the set of pursued orders. Given that the dimensionality of a mixed‐integer linear programming formulation of the problem increases exponentially with the number of potential orders, we develop both a tailored exact algorithm based on the L‐shaped method for two‐stage stochastic programming as well as a heuristic method. We also extend our solution approach to account for piecewise‐linear cost and revenue functions as well as a multiperiod setting. Extensive experimentation indicates that our exact approach rapidly finds optimal solutions with three times as many orders as a state‐of‐the‐art commercial solver. In addition, our heuristic approach provides average gaps of less than 1% for the largest problems that can be solved exactly. Observing that the gaps decrease as problem size grows, we expect the heuristic approach to work well for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008

Are Trading Costs Invisible in Trading Decisions?

This article examines whether professional traders recognize transaction costs when making trade decisions. In both single and multi-period settings, professional traders are far more reluctant to realize a gross loss than an actual loss (net of transaction costs). The tendency to ignore transaction costs may lead to higher levels of overconfidence (or trading activity) because traders are more susceptible to misinterpreting negative performance outcomes than positive ones. Traders who experience higher and more frequent gross trading profits trade more actively, but they also end up losing the most money on a net basis.

Relative Performance Evaluation: Does Reducing Exposure to Common Risks Provide Performance Benefits in Multi-period Settings?

Extant research suggests relative performance evaluation increases performance in single-period settings. The principal mechanism for this increase is relative performance evaluation’s ability to reduce exposure to common risks. However, I predict that in multi-period settings this reduction in exposure to common risks will not increase performance. In a laboratory experiment, I isolate the performance effects of reducing common risks and find that the benefits do not persist in multi-period settings. This occurs because individuals who fail in the current period attribute that failure to reasons they believe are more likely to affect future periods. Thus, they lower their expectancy. Expectancy’s positive correlation with future period effort and performance means that future period performance does not increase for individuals who fail in the current period. These findings suggest that we focus attempts to improve the multi-period performance effectiveness of relative performance evaluation on its other benefits.

Are Trading Costs Invisible in Trading Decisions?

We examine whether or not professional traders recognize transaction costs when making trade decisions. In both single and multi-period settings, professional traders are far more reluctant to realize a gross loss rather than an actual loss (net of transaction costs). The tendency to ignore transaction costs leads to higher levels of overconfidence (or trading activity) because traders are more susceptible to misinterpret negative performance outcomes for positive ones. We find that traders who experience higher and more frequent gross trading profits trade more actively, but they also end up losing the most money on a net basis.

General Pareto Optimal Allocations and Applications to Multi-Period Risks

In this paper, we consider the problem of Pareto optimal allocation in a general framework, involving preference functionals defined on a general real vector space. The optimization problem is equivalent to a modified sup-convolution of the different agents’ preference functionals. The results are then applied to a multi-period setting and some further characterization of Pareto optimality for an allocation is obtained for expected utility for processes.

General Pareto Optimal Allocations and Applications to Multi-Period Risks

In this paper, we consider the problem of Pareto optimal allocation in a general framework, involving preference functionals defined on a general real vector space. The optimization problem is equivalent to a modified sup-convolution of the different agents’ preference functionals. The results are then applied to a multi-period setting and some further characterization of Pareto optimality for an allocation is obtained for expected utility for processes.

Local Cross Entropy in a Multi-Period Setting

Local Cross Entropy in a Multi-Period Setting

A Factor Allocation Approach to Optimal Bond Portfolio

This paper proposes a new method to a bond portfolio problem in a multi-period setting. In particular, we apply a factor allocation approach to constructing the optimal bond portfolio in a class of multi-factor Gaussian yield curve models. In other words, we consider a bond portfolio problem in terms of a factors’ allocation problem. Thus, we can obtain clear interpretation about the relation between the change in the shape of a yield curve and dynamic optimal strategy, which is usually hard to be obtained due to high correlations among individual bonds. We first present a closed form solution of the optimal bond portfolio in a class of the multi-factor Gaussian term structure model. Then, we investigate the effects of various changes in the term structure on the optimal portfolio strategy through series of comparative statics.

Integrated Optimization of Procurement, Processing and Trade of Commodities in a Network Environment

We consider the integrated optimization problem of procurement, processing and trade of commodities over a network in a multiperiod setting. Motivated by the operations of a prominent commodity processing flrm, we model a flrm that operates a star network with multiple locations at which it can procure an input commodity and has processing capacity at a central location to convert the input into a processed commodity. The processed commodity is sold using forward contracts, while the input itself can be traded at the end of the horizon. We show that the single-node version of this problem can be solved optimally when the procurement cost for the input is piecewise linear and convex, and derive closed form expressions for the marginal value of input and output inventory. However, these marginal values are hard to compute because of high dimensionality of the state space and we develop an e‐cient heuristic to compute approximate marginal values. We also show that the star network problem can be approximated as an equivalent single node problem and propose heuristics for solving the network problem. We conduct numerical studies to evaluate the performance of both the single node and network heuristics. We flnd that the single node heuristics are near-optimal, capturing close to 90% of the value of an upper bound on the optimal expected proflts. Approximating the star network by a single node is efiective, with the gap between the heuristic and upper bound ranging from 7% to 14% for longer planning horizons.

Implications of the Sharpe ratio as a performance measure in multi-period settings

We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic market. We demonstrate that the manager's focus on the short horizon is detrimental to the long-horizon investor. When the returns are iid, the performance loss is significant, even when horizons are not very different. When the returns are mean reverting, the performance loss is exacerbated. We show that the manager's strategy tends to increase (decrease) the risk in the latter part of the optimization period after a bad (good) performance in the earlier part of the period, in agreement with empirical observations.

Varying the VaR for unconditional and conditional environments

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from 12 European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates accounting for volatility clustering are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.

Dynamic Equilibrium Valuation of Electricity Futures

We propose a dynamic competitive equilibrium model for pricing electricity futures. With exogenous demand and a convex function of marginal production cost, we endogenously receive a term structure of futures prices and futures price premia. The multi-period setting enables us to receive the futures price evolution until maturity and to evaluate cascade futures as they are common e. g. at Nord Pool and the European Energy Exchange. Our model allows to incorporate seasonality of electricity demand which is a major component of electricity prices. A comprehensive comparative static analysis concludes our paper.

Regime switching based portfolio selection for pension funds

This paper shows how a mean variance criterion can be applied to a multi period setting in order to obtain efficient portfolios in an asset and liability context. The optimization model allows for rebalancing activities, transaction costs, stochastic volatilities for both assets and liabilities. Furthermore, a general framework for the projection of pension fund liabilities as well as for the generation of asset returns is given. In a further step the dynamics of the liability maturity structure is modeled as customized index, whose volatility and correlation with asset returns become integral components of the applied regime switching approach. The numerical results illustrate the diversification of the assets and its risk return pattern in dependency of the liability dynamics.