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AbstractThis paper presents an extension of gold‐mining problems formulated in earlier work by R. Bellman and J. Kadane. Bellman assumes there are two gold mines labeled A and B, respectively, each with a known initial amount of gold. There is one delicate gold‐mining machine which can be used to excavate one mine per day. Associated with mine A is a known constant return rate and a known constant probability of breakdown. There is also a return rate and probability of breakdown for mine B. Bellman solves the problem of finding a sequential decision procedure to maximize the expected amount of gold obtained before breakdown of the machine. Kadane extends the problem by assuming that there are several mines and that there are sequences of constants such that the jth constant for each mine represents the return rate for the jth excavation of that mine. He also assumes that the probability of breakdown during the jth excavation of a mine depends on j. We extend these results by assuming that the return rates are random variables with known joint distribution and by allowing the probability of breakdown to be a function of previous observations on the return rates. We show that under certain regularity conditions on the joint distributions of the random variables, the optimal policy is: at each stage always select a mine which has maximal conditional expected return per unit risk. This gold‐mining problem is also a formulation of the problem of time‐sequential tactical allocation of bombers to targets. Several examples illustrating these results are presented.

Abstract Political economy literature highlights the tactical use of intergovernmental grants for electoral purposes; however, it provides different mechanisms and explanations behind these patterns. In this paper, we propose a model that includes 3 branches of the literature in order to provide a comprehensive explanation behind the tactical allocation by central governments. We identify 3 key parameters that shape the tactical allocation of grants: the electoral rule, the relative importance of the objective of the central government with respect to the local government, and the extent to which citizens attribute local expenditure to the direct action of the local government vs the central government (local political appropriability). In addition, our model also provides a guideline for designing and interpreting empirical results on the tactical allocation of grants distribution.

The mathematical theory of differential games is used to study the structure of optimal allocation strategies for some time-sequential combat games with combat described by Lanchester-type equations of warfare. As required by such applications, some new theoretical results are given: first order necessary conditions of optimality are developed for differential games with state variable inequality constraints. These results are used to study optimal air-war strategies in a differential game model. In a different model, optimal air-war strategies are further studied within the context of land-war objectives. Optimal fire-support strategies are studied in an attack scenario with a differential game model. A comprehensive survey of previous literature on each of the above topics is given. Finally, some problems for possible future study are discussed. ; supported by Naval Analysis Programs, Office of Naval Research under ONR Project Order PO-4-0174 and Task Number NR 276-039. ; http://archive.org/details/applicationofdif4051tayl ; 61153 N; RR614-11-05; NR 276-039; PO-4-0174 ; NA

Nevertheless, this peculiarity of the Spanish political system did not eliminate the incentives for governments to use pork-barrel policies. On the one hand, despite electoral results being centrally planned, Madrid's limited capacity to intervene in society implied that elections outcomes had to be negotiated with the local elites, who demanded compensations (such as public funds) for their districts' electoral support. On the other hand, the two-party system may be seen as a duopoly regime, in which opposition districts were actually those which did not respect the alternation system, and voted for either the dynastic party that was going to lose the election or for a third political force. Restoration Spain provides therefore an interesting case of a political system in which a dominating duopoly used pork-barrel strategies to persuade the electorate to change the sign of their votes in every electoral call. In this setting, two kinds of political economy models may be relevant to analyze pork-barrel in Restoration Spain. One can see the Spanish Restoration as a semi-democratic regime ruled by a duopoly that furthered its political goals by using the geographical allocation of public resources. More specifically, governments showered resources on those districts that were loyal to the alternation system, and starved the rebellious ones. This would be similar to a typical semi-democratic system, although one in which the hegemonic political force was not a single party but a duopoly. On the other hand, given the importance of local elites, non-partisan motivations may also offer a partial description of the political process. In non-partisan models, the distribution of public funds reflects the influence and ability of individual MPs, who compete for administrative resources to reinforce their links with their electorates. Indeed, bringing home the pork increases MPs' reputation with local elites (Levitt and Snyder, 1995; Levitt and Poterba, 1999; Milligan and Smart, 2005).

[eng] Nevertheless, this peculiarity of the Spanish political system did not eliminate the incentives for governments to use pork-barrel policies. On the one hand, despite electoral results being centrally planned, Madrid's limited capacity to intervene in society implied that elections outcomes had to be negotiated with the local elites, who demanded compensations (such as public funds) for their districts' electoral support. On the other hand, the two-party system may be seen as a duopoly regime, in which opposition districts were actually those which did not respect the alternation system, and voted for either the dynastic party that was going to lose the election or for a third political force. Restoration Spain provides therefore an interesting case of a political system in which a dominating duopoly used pork-barrel strategies to persuade the electorate to change the sign of their votes in every electoral call. In this setting, two kinds of political economy models may be relevant to analyze pork-barrel in Restoration Spain. One can see the Spanish Restoration as a semi-democratic regime ruled by a duopoly that furthered its political goals by using the geographical allocation of public resources. More specifically, governments showered resources on those districts that were loyal to the alternation system, and starved the rebellious ones. This would be similar to a typical semi-democratic system, although one in which the hegemonic political force was not a single party but a duopoly. On the other hand, given the importance of local elites, non-partisan motivations may also offer a partial description of the political process. In non-partisan models, the distribution of public funds reflects the influence and ability of individual MPs, who compete for administrative resources to reinforce their links with their electorates. Indeed, bringing home the pork increases MPs' reputation with local elites (Levitt and Snyder, 1995; Levitt and Poterba, 1999; Milligan and Smart, 2005).

The mathematical theory of deterministic optimal control/differential games is applied to the study of some tactical allocation problems for combat described by Lanchester-type equations of warfare. A solution procedure is devised for terminal control attrition games. H. K. Weiss' supporting weapon system game is solved and several extensions considered. A sequence of one-sided dynamic allocation problems is considered to study the dependence of optimal allocation policies upon model form. The solution is developed for variable coefficient Lanchester-type equations when the ratio of attrition rates is constant. Several versions of Bellman's continuous stochastic gold-mining problem are solved by the Pontryagin maximum principle, and their relationship to the attrition problems is discussed. A new dynamic kill potential is developed. Several problems from continuous review deterministic inventory theory are solved by the maximum principle. ; The Office of Naval Research ; http://archive.org/details/applicationofdif00tayl ; NA

The mathematical theory of optimal control/differential games is used to study the structure of optimal allocation policies for some tactical allocation problems with combat described by Lanchester-type equations of warfare. Both deterministic and stochastic attrition processes are considered. For the optimal control of deterministic Lanchester-type attrition process, a general solution algorithm for the synthesis of the optimal policy is developed. Optimal allocation policies are developed for numerous one-sided optimization problems of tactical interest in order to study the dependence of the structure of these optimal policies on model form. Consideration has been given to singular extremals, multiple extremals (including dispersal surfaces), and state variable inequality constraints. It is shown how to apply the theory of state variable inequality constraints to determine the optimal control of deterministic Lanchester-type processes in order to treat non-negativity restrictions on force levels and thus to study the dependence of optimal policies upon the force levels. Various attrition models are considered (reflecting different assumptions as to target acquisition process, command and control capabilities, target engagement process, variations in range capabilities of weapon systems). Solutions are developed for Lanchester-type equations of modern warfare with variable attrition-rate coefficients. The optimal control of the Lanchester stochastic process is studied. (Author) ; Naval Analysis Programs, Office of Naval Research under ONR Project Order PO2-0150 and Task Number NR 276-039. ; http://archive.org/details/applicationofdif2111tayl ; Research sponsored by Naval Analysis Programs, Office of Naval Research under ONR Project Order P02-0150 and Task Number NR 276-039 -- Cover. ; NA

The mathematical theory of differential games is used to study the structure of optimal allocation strategies for some time-sequential combat games with combat described by Lanchester-type equations of warfare. Several specific problems for the determination of optimal time-sequential fire distribution strategies for supporting weapon systems are studied. Optimal air-war strategies are studied within the context of land-war objectives and compared to those for a model which does not explicitly consider the ground war. Several differential game models are used to study optimal fire-support strategies in an attack scenario. For an existing differential game fire-support model we determine for what class of criterion functionals (i.e., objectives) the optimal fire-support strategies are independent of force levels. In a similar differential game we examine the dependence of optimal fire-support strategies upon the functional form of the combat attrition model by considering slightly different combat dynamics. Some relatively new theoretical developments are required for the complete solution of this latter problem. Previous analytic work in the field of determination of optimal fire-support strategies is reviewed. ; supported by Naval Analysis Programs, Office of Naval Research partially under ONR Research Project RR014-11-01 (NR 277-087) and partially under ONR Project Order PO-4-0174 and Task Number NR 276-039. ; http://archive.org/details/applicationofdif4112tayl ; NA

AbstractMarket events of the past ten years have sparked an interest in tactical asset allocation. In the current study we develop and test a model that incorporates currently available information into the tactical asset allocation process. The model provides an estimate of the probabilities that the upcoming market period will be bullish or bearish. Logit analysis is employed to determine which of the various timely and readily available data significantly affect these probabilities. These estimated probabilities are used to suggest the optimal allocations of funds over time between the risk‐free asset and the market portfolio. Then, several timing strategies are compared with a buy‐and‐hold portfolio. An asset allocation strategy based on the probabilities assigned by the logit model appears to achieve greater terminal wealth with less variability of returns. Similar results are obtained for both an initial sample (1962–76 in our model) and a holdout sample (1977–88).

This book covers each step in the asset allocation process, addressing as many of the relevant questions as possible along the way. How can we formulate expectations about long-term returns? How relevant are valuations? What are the challenges to optimizing the portfolio? Can factor investing add value and, if so, how can it be implemented? Which are the key performance drivers for each asset class, and what determines how they are correlated? How can we apply insights about the business cycle to tactical asset allocation? The book is aimed at finance professionals and others looking for a coherent framework for decision-making in asset allocation, both at the strategic and tactical level. It stresses analysis rather than pre-conceived ideas about investments, and it draws on both empirical research and practical experience to give the reader as strong a background as possible.--