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Cemeteries in the UK and Ireland are typically viewed as a final 'place of rest' for the deceased where their remains will not be disturbed. This sense is at least in some part created by the norm of in-perpetuity grave rights in these countries. Yet while 'in-perpetuity' suggests fixity, it is defined and managed in varying ways in different settings, including an ultimate fixed term for some graves and cemeteries. Over decades, in-perpetuity cemeteries and cemetery policies adapt to and reflect changes in cultural trends, national and local politics, cemetery management, planning, regeneration, and other pressures on land, as well as the changes that occur in the natural environment in which they are situated. In this article, we explore the rhythms and temporalities of cemeteries characterised by in-perpetuity grave rights, by looking at how the tensions between perpetuity and change are perceived, experienced, and managed by burial service staff and varied communities who use them. In-perpetuity grave rights impact the management of cemeteries, their material form, and how they are used. A focus on the temporalities and rhythms of cemeteries in the UK and Ireland enables a reconsideration of the concepts of perpetuity and change in death and remembrance. [ABSTRACT FROM AUTHOR]

Muslims, inspired by numerous divine principles, have established the culture of infāq by founding charitable institutions in diverse geographies throughout history. One of the most reputable institutions for cultivating this culture is unquestionably endowment. This institution has made great contributions to strengthening the social and economic ties of the believers and to forming their cultural and spiritual identities from the beginning of the asr al-sa‘ādah until today. Therefore, it is vital to update the theoretical understanding of endowments, draw insights from various precedents and improve the effectiveness of practical applications accordingly. There is no verse in the Qur'an explicitly stating the legitimacy of endowments; however, the verses encouraging charity and competing in good deeds form the basis of the institution of endowments. Very few rulings on endowments are determined by the Sunnah; the majority come from the jurisprudence of the jurists, based on the evidence of istiẖsān, istiṣlāẖ and ‘urf. Jurists agree that endowments are legitimate, but their views diverge on which assets may qualify as the subject of an endowment. They unanimously accept that immovable property such as lands, houses, and shops can be endowed. However, they disagree about the endowment of movable properties. Some jurists stipulate the characteristic of "perpetuity". While some jurists deem the endowment of movable properties to be absolutely permitted, others considerit permissible only under specific circumstances. Movable properties are classified into two categories regarding endowment status: “movables that retain their original form after usufruct” even for a certain period, and “movables that do not retain their original form after usufruct”. According to H̱anafī jurists, “perpetuity” is the general rule/reference for endowment. They argue that movables cannot be endowed in absolute terms because they do not conform to this general rule. However, they make three exceptions to this general understanding, and accept the endowment of movables falling under these categories as authentic. Early H̱anafīs deemed the endowment of dīnārs, dirhams, makīlāt, and mawzūnāt to be authentic. Shāfi‘ī scholars state that the condition of “perpetuity” is absolutely attained in properties such as land, and as long as their lifespan in properties such as books, horses, and weapons. From this perspective, they deem it permissible to endow movable properties that can be used for a certain period and do not lose their original qualities immediately. However, they do not accept the endowment of movables such as foodstuffs which are consumed through usufruct and cannot be utilized even for a certain period. The majority of H̱anbalīscholars agree with the Shāfi‘ī jurists. Some H̱anbalīs, however, view the endowment of movable properties whose original qualities are lost by usufruct as legitimate if there exists an established practice and legal precedent. The most comprehensive stance on endowment property is that of Mālikī scholars. They do not stipulate the condition of perpetuity in endowments and recognize that endowments can also be of a temporary nature. Therefore, it is permissible to endow cash, foodstuffs, books, clothes, and similar movable property of both classes. In the case of movable perpetual property, the solution is "istibdâl". The Imamiyya share the same view as the Mālikīs. We observe that the Mālikī view is preferred in legal regulations in the Islamic world and in the decisions of fatwa councils. In this context, the opinions of jurists, decisions of fatwā councils, historical practices and practices in Islamic states are analyzed to present an opinion on making the endowment institution more functional. [ABSTRACT FROM AUTHOR]

The fires of the Jerusalem temple altar were said to be perpetual. Various writers from the fourth century BCE to the third century CE added explanations and perspectives to this practice: the argument that the fire came from heaven, that it continued even during the destruction of the temple, or that it remained lit only when the high priest was righteous. Though these texts are well known, they were never examined in a comparative context: how special were these practices and discourses in their Mediterranean and Persian contexts? Maintaining a perpetual fire on the altar or lamps was a known practice in Mediterranean sanctuaries. The discourses surrounding these fires, developed especially by Greek and Roman writers of the first century BCE and the first century CE, are in many ways similar to those in the Jewish texts. I will consider in detail the differences and similarities and their significance. [ABSTRACT FROM AUTHOR]

In distributional reinforcement learning (RL), not only expected returns but the complete return distributions of a policy are taken into account. The return distribution for a fixed policy is given as the solution of an associated distributional Bellman equation. In this note, we consider general distributional Bellman equations and study the existence and uniqueness of their solutions, as well as tail properties of return distributions. We give necessary and sufficient conditions for the existence and uniqueness of return distributions and identify cases of regular variation. We link distributional Bellman equations to multivariate affine distributional equations. We show that any solution of a distributional Bellman equation can be obtained as the vector of marginal laws of a solution to a multivariate affine distributional equation. This makes the general theory of such equations applicable to the distributional reinforcement learning setting.

In distributional reinforcement learning (RL), not only expected returns but the complete return distributions of a policy are taken into account. The return distribution for a fixed policy is given as the solution of an associated distributional Bellman equation. In this note, we consider general distributional Bellman equations and study the existence and uniqueness of their solutions, as well as tail properties of return distributions. We give necessary and sufficient conditions for the existence and uniqueness of return distributions and identify cases of regular variation. We link distributional Bellman equations to multivariate affine distributional equations. We show that any solution of a distributional Bellman equation can be obtained as the vector of marginal laws of a solution to a multivariate affine distributional equation. This makes the general theory of such equations applicable to the distributional reinforcement learning setting. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Islamic Review / İslam Tetkikleri Dergisi is the property of Journal of Islamic Review and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Larq Journal for Philosophy, Linguistics & Social Sciences is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We use a payment pattern of the type { 1 k , 2 k , 3 k , ... } to generalize the standard level payment and increasing annuity to polynomial payment patterns. We derive explicit formulas for the present value of an n-year polynomial annuity, the present value of an m-monthly n-year polynomial annuity, and the present value of an n-year continuous polynomial annuity. We also use the idea to extend the annuities to payment patterns derived from analytic functions, as well as to payment patterns of the type { 1 r , 2 r , 3 r , ... } , with r being an arbitrary real number. In the process, we develop possible approximations to k ! and for the gamma function evaluated at real numbers. [ABSTRACT FROM AUTHOR]

The paper explores the economic opportunities of growing fast-growing plants for bioenergy production and use. Based on primary data of the above-ground dry biomass of the Miscanthus × giganteus, from the experimental field of Kolíňany, the average yield during the life cycle of the crop was 33.31 t/ha (stand. dev. 7.07). The next step was assembling the economic model of gross financial yield based on using the biomass for the production of bioenergy. Using the Discounted Cash-flow model, the gross financial yield, neglecting the costs, was set to 1547 €/ha. Finally, adjusting for the growing conditions of the Miscanthus, we set the gross financial yield as a deferred annuity to 3036.93 €/ha per one life cycle of the crop.

Copyright of Lusíada. Economia & Empresa is the property of Fundacao Minerva-Cultura-Ensino e Investigacao Cientifica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Linear fractional Galton–Watson branching processes in i.i.d. random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals. On the other hand, any random difference equation defines an autoregressive Markov chain (a random affine recursion) which can be positive recurrent, null recurrent and transient and which, as the forward iterations of an iterated function system, has an a.s. convergent counterpart in the positive recurrent case given by the corresponding backward iterations. The present expository article aims to provide an explicit view at how these aspects of random difference equations and their stationary limits, called perpetuities, enter into the results and the analysis, especially in quenched regime. Although most of the results presented here are known, we hope that the offered perspective will be welcomed by some readers. [ABSTRACT FROM AUTHOR]

The article questions what allows some of the actors in archaeology to attribute the term archaeological to the observations and remains they discover and describe. This contribution to the debate on “archaeologicity” is innovative and mobilizes concepts from the sociology of organizations and management sciences. The authors assert that there is a process of legitimization specific to the field of archaeology, whose actors have leeway to make some “bricolage” with this process, which thus enables institutions of the field to ensure the perpetuity of their legitimacy.

We study the stochastic recursion X n = Ψ n (X n − 1) , where (Ψ n) n ≥ 1 is a sequence of i.i.d. random Lipschitz mappings close to the random affine transformation x ↦ A x + B. We describe the tail behaviour of the stationary solution X under the assumption that there exists α > 0 such that E | A | α = 1 and the tail of B is regularly varying with index − α < 0. We also find the second order asymptotics of the tail of X when Ψ (x) = A x + B. [ABSTRACT FROM AUTHOR]

Muslim jurists differed in the declaration (sighah) of waqf, specifically on whether a waqf can be made temporary or it is limited to perpetuity. The objectives of this paper are: to critically examine the concept of temporary waqf, to assess the different opinions of the scholars on the issue of temporary waqf and to discuss the evidences relied upon every doctrine, to explore the public interest (maslahah) of contemporary application. A qualitative methodology was employed to analyse the data through inductive and deductive methods. The inductive and deductive methods were used to research the main sources of literatures and to analyse the issues related to the temporary waqf. The findings have shown that an essential features of waqf is not limited only to perpetuity, hence some jurists such as Maliki school of Islami law approves the application of temporary and perpetual waqf. Thus, there is a need for temporary waqf to be enacted and applied as it provides the best interests of donors, beneficiaries and community at large. Impliedly, Islamic legal pronouncements (fatwa’s) which were issued by the State Fatwa Committee in Malaysia should not be limited to the view of a single school of Islamic law, especially in the field of waqf

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten–Goldie setting but involve a logarithmic term. [ABSTRACT FROM AUTHOR]

Copyright of Alkemie is the property of Classiques Garnier and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Academics and practitioners have been applying equity valuation methods mainly based on discount cash flow models, residual income models, or dividend discount models combined with balance sheet and income statement multiples of market comparables to analyse share price, provide price targets for investors, or even as a basis for transactions such as mergers and acquisitions (M&A). Most of these methods rely on mathematical deductions of growing or constant perpetuities or near perpetuities (such as annuities) to attain market values. However, it is of the utmost relevance for valuation to verify how the theoretical models relate with real values, and what their relationship is with companies' past age. Beyond stating a non-linear relationship for valuation models and ascertain important valuation drivers, using a sample of more than 3,400 European companies with cross section data, this paper contributes to the improvement of valuation model's effectiveness by inducing non-explicit period valuation modifications to long-term annuities and perpetuities, considering class age intervals. This paper's originality is supported by the study of the relationship of past company age with predicted annuities, the proof of non-compliance of perpetuity-based valuation models, and the contribution of new value drivers for valuation purposes. [ABSTRACT FROM AUTHOR]

Copyright of Turkish Journal of Social Research / Turkiye Sosyal Arastirmalar Dergisi is the property of Turkish Journal of Social Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We provide three disjoint groups of sufficient conditions which ensure that the right tail of a perpetuity ℙ{ X > x } is asymptotic to ax c e- bx as x → ∞ for some a , b > 0, and c ∈ ℝ. Our results complement those of Denisov and Zwart (2007). As an auxiliary tool we provide criteria for the finiteness of the one-sided exponential moments of perpetuities. We give several examples in which the distributions of perpetuities are explicitly identified. [ABSTRACT FROM AUTHOR]

Copyright of Romanian Journal of Compulsory Execution / Revista Română de Executare Silită is the property of Universul Juridic Publishing House and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This is a teaching case that involves Natura S.A.'s (a cosmetic company headquartered in Cajamar, S. Paulo, Brazil) valuation. Alberto Sena and Luiza Spulet have the mission of valuing it for Mr. Charles Ian Jones, manager of an investment fund headquartered in New York. The dilemma addressed is restricted to the assumptions to be adopted for the perpetuity calculation. The remaining assumptions, simplified, are outlined in the text of the case. The recommendation is that the teaching case be applied in disciplines of corporate finance or valuation in undergraduate, specialization or postgraduate courses. The purpose of the case is to explore the possibilities of assumption to calculate the perpetuity, providing an environment for the conceptual discussion involving the correct application of the Gordon and Shapiro's (1956) model. It is hoped, with its application, that students understand that applying the mentioned model inadvertently may result in distorted and far from reality values. The teacher/instructor can use the case beyond its original purpose (perpetuity calculation), applying it to explore all the stages of valuation and their respective points of controversy, exploring other (1) operational assumptions for the company and (2) cost of capital assumptions. [ABSTRACT FROM AUTHOR]

We prove weak convergence on the Skorokhod space of Galton–Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. The limits are extremal shot noise processes. By considering marginal distributions, we recover the results of Pakes (1979). [ABSTRACT FROM AUTHOR]

Given a sequence (Mk, Qk)k ≥ 1 of independent and identically distributed random vectors with nonnegative components, we consider the recursive Markov chain (Xn)n ≥ 0, defined by the random difference equation Xn = MnXn - 1 + Qn for n ≥ 1, where X0 is independent of (Mk, Qk)k ≥ 1. Criteria for the null recurrence/transience are provided in the situation where (Xn)n ≥ 0 is contractive in the sense that M1 ⋯ Mn → 0 almost surely, yet occasional large values of the Qn overcompensate the contractive behavior so that positive recurrence fails to hold. We also investigate the attractor set of (Xn)n ≥ 0 under the sole assumption that this chain is locally contractive and recurrent. [ABSTRACT FROM AUTHOR]

Let ( ξ , η ), ( ξ , η ),... be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the J -topology on the Skorokhod space of $n^{-1/2}\underset {0\leq k\leq [n\cdot ]}{\max }\,(\xi _{1}+\ldots +\xi _{k}+\eta _{k+1})$ was proved under the assumption that contributions of $\underset {0\leq k\leq n}{\max }\,(\xi _{1}+\ldots +\xi _{k})$ and $\underset {1\leq k\leq n}{\max }\,\eta _{k}$ to the limit are comparable and that n ( ξ +... + ξ ) is attracted to a Brownian motion. In the present paper, we continue this line of research and investigate a more complicated situation when ξ +... + ξ , properly normalized without centering, is attracted to a centered stable Lévy process, a process with jumps. As a consequence, weak convergence normally holds in the M -topology. We also provide sufficient conditions for the J -convergence. For completeness, less interesting situations are discussed when one of the sequences $\underset {0\leq k\leq n}{\max }\,(\xi _{1}+\ldots +\xi _{k})$ and $\underset {1\leq k\leq n}{\max }\,\eta _{k}$ dominates the other. An application of our main results to divergent perpetuities with positive entries is given. [ABSTRACT FROM AUTHOR]

The stability of iterations of affine linear maps Ψn(x)=Anx+Bn,n=1,2,... is studied in the presence of a Markovian environment, more precisely, for the situation when (An,Bn)n≥1 is modulated by an ergodic Markov chain (Mn)n≥0 with countable state space SS and stationary distribution ππ. We provide necessary and sufficient conditions for the a.s. and the distributional convergence of the backward iterations Ψ1O...OΨn(Z0) and also describe all possible limit laws as solutions to a certain Markovian stochastic fixed-point equation. As a consequence of the random environment, these limit laws are stochastic kernels from SS to RR rather than distributions on RR, thus reflecting their dependence on where the driving chain is started. We give also necessary and sufficient conditions for the distributional convergence of the forward iterations ΨnO...OΨ1. The main differences caused by the Markovian environment as opposed to the extensively studied case of independent and identically distributed (iid) Ψ1,Ψ2,... are that: (1) backward iterations may still converge in distribution if a.s. convergence fails, (2) the degenerate case when A1cM1+B1=cM0 a.s. for suitable constants cici, i∈S, is by far more complex than the degenerate case for iid (An,Bn) when A1c+B1=cA a.s. for some c∈R, and (3) forward and backward iterations generally have different laws given M0=i for i∈S so that the former ones need a separate analysis. Our proofs draw on related results for the iid-case, notably by Vervaat, Grincevičius, and Goldie and Maller, in combination with recent results by the authors on fluctuation theory for Markov random walks. [ABSTRACT FROM AUTHOR]