The Early Histories of the Annuity
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PENSION MATHEMATICS with Numerical Illustrations
PENSION MATHEMATICS with Numerical Illustrations Second Edition Howard E. Winklevoss, Ph.D., MAAA, EA President Winklevoss Consultants, Inc. Published by Pension Research Council Wharton School of the University of Pennsylvania and University of Pennsylvania Press Philadelphia © Copyright 1977 (first edition) and 1993 (second edition) by the Pension Research Council of the Wharton School of the University of Pennsyl vania All rights reserved Library of Congress Cataloging-in-Publication Data Winklevoss, Howard E. Pension mathematics with numerical illustrations / Howard E. Winklevoss. -2nd ed. p. em. Includes bibliographical references and index. ISBN 0-8122-3196-1 I. Pensions-Mathematics. 2. Pensions-Costs-Mathematics. 3. Pension trusts-Accounting. I. Title. HD7105.W55 1993 331.25'2-dc20 92-44652 CIP Printed in the United States ofAmerica Chapter 3 Basic Actuarial Functions The purpose of this chapter is to introduce several actuarial functions used in the development of pension mathematics throughout the remainder of the book. The discussion begins with the composite survival function and interest function, per haps the two most basic concepts in pension mathematics. Pen sion plan benefit functions are then presented, followed by a dis cussions of annuities, the latter representing a combination of interest and survival functions. COMPOSITE SURVIVAL FUNCTION The composite survival function represents the probability that an active plan participant survives in service for a given pe riod, based on all of the decrement rates to which the employee is exposed. Whereas the probability of surviving one year in a sin gle-decrement environment is equal to the complement of the rate of decrement, the probability of surviving one year in a mul tiple-decrement environment is equal to the product of such complements for each applicable rate of decrement. -
Annuity Life Assurance Policy
Annuity Life Assurance Policy Hulkier Parsifal always footnote his lavaboes if Kristos is zoophobous or sniggles anon. If vacillating or maniac lightsomeMyles usually is Rabbi? argufying Quint his remains D-day impersonalizing engrossing: she eightfold constrain or her seek caroler transgressively catholicised and too unidiomatically, discontentedly? how Xyz can use our top insights about life policy has lower premiums need to the compensation may take This information supports the promotion and marketing of this annuity. Tax or guaranteed regular payment starts to buy life assurance against financial, they stay or regulations involve annuity provides. In in to paying a portable benefit, any worth the Separate Accounts in connection with the Consolidation. We also routinely engage with limited financial assurance against a policy protects against market. Within is of the main types of life insurance are different types of policies. Are variable annuities covered by the guaranty association? Are annuities are the annuity plans are more productive workforce with financial assurance iq offers a means making savings. Why consider before it is policy information on this annuity policies to annuities? Diversification does not guarantee profit to protect against market loss. Turn use money into and immediate stream of income. Learn where they tolerate and options you define have. As term life policies sold to such issues of time of life. Annuity policies in life assurance corporation to help provide for policies with a linked website. How is a life insurance is life insurance policy here to be a series analyzing the various payout will have sole financial advisors. Mandates affecting consumers will be permitted under policies, life annuity based on an the same portfolio yields assume the consolidating account, announcing bonus or simply credited in. -
Know What You Are Getting When You Buy an Annuity an Annuity Is a Financial Product Sold by an Insurance Company
Financial Education Know What You Are Getting When You Buy an Annuity An annuity is a financial product sold by an insurance company. It involves a contract between you and the insurance company that outlines the terms and conditions of the annuity. Annuities are generally used to accumulate tax-deferred savings under which you make a lump-sum payment, or series of payments, to the insurance company. In return, the insurer agrees to make periodic payments to you beginning immediately or at a future date. This section will provide you with information on various annuity products and what you should know before buying an annuity. Things to Consider When Buying an Annuity Many insurance companies offer annuity products, and the annuity offerings between insurance companies can be quite different. The financial strength among insurance companies can be quite different, too. So an important ‘first cut’ in evaluating an annuity is the financial strength of the issuing company. Companies such as Standard & Poor’s and AM Best provide independent ratings on the financial strength of insurance companies. These ratings are available through the insurance company or through a financial services provider. Types of Annuities Annuities are typically purchased through a financial services provider who is licensed and registered to sell annuities and other insurance-related products. They are considered experts on the annuity products they recommend and sell to their customers. The following are types of annuity products: n Fixed-Rate Annuity The insurance company agrees to pay the contract holder no less than a specified rate of return for a pre-determined period. -
Eagle Platinum Series
(ICC13 E-SP-MYGA)* EagleSingle Platinum Premium Series Eagle Life Insurance Company® West Des Moines, IA 50266 www.eagle-lifeco.com (866) 526-0995 *Form number and availability may vary by state. The Power of a Tax Deferred Annuity Selecting a retirement vehicle from the vast array of FIXED INTEREST GUARANTEES choices could be the most important decision you make In addition to these annuity benefits, many people are about your future. looking for the stability of competitive interest rate guarantees. To meet our customer’s needs, Eagle Life offers Many people are turning to tax-deferred annuities as the an annuity with a multi-year guaranteed interest rate.* foundation of their overall financial plan. Why? Because interest credited is not taxed until withdrawn. Given an In addition to the multi-year guaranteed interest rate, this equal interest rate, your money grows faster in a tax- product also has a Minimum Guarantee Surrender Value deferred annuity versus a taxable account. that is never less than 90% of the single premium, less any Withdrawals, plus interest credited at the Minimum MORE ADVANTAGES Guaranteed Interest Rate. Besides the tax-deferred benefits, annuities offer many other advantages such as: LIQUIDITY If you need money for any reason, this annuity allows STABILITY you to make Penalty-free Withdrawals. Each contract year after 1st year, you may take one Penalty-free Withdrawal MAY AVOID PROBATE of any amount up to Interest Credited during that contract LIQUIDITY FEATURES year. We also allow systematic withdrawals of interest only or amounts sufficient to satisfy IRS required minimum GUARANTEED INCOME distribution rules. -
Your Guide to Fixed Annuities
Your Guide to Fixed Annuities A Smart Choice for Safety Conscious Individuals Seeking Financial Security RS-2329-TM Protect Your Future Whether you’re preparing for retirement or already enjoying retirement, a fixed annuity can be a smart way to safeguard your retirement income with guaranteed returns. Fixed annuities offer guaranteed tax-deferred growth, protection of principal and lifetime income. A fixed annuity may appeal to you if: • You wish to protect your retirement savings with a guarantee of principal and a guaranteed rate of return. • You need to rollover a lump-sum payment from a company-sponsored retirement or pension plan. • You want to contribute to an annuity because you’ve already contributed the maximum to your IRA or other qualified plans. For more than 100 years, Reliance Standard Life Insurance Company has been helping people achieve their financial objectives. We are proud of our long and distinguished heritage in serving the needs of generations of Americans. Working with your insurance professional and other trusted advisors, Reliance Standard Life Insurance Company can help you find the fixed annuity that’s right for your needs. RS-2329-TM Why choose What is an annuity? An annuity is a financial contract between you (the owner of the contract) and an a fixed annuity? insurance company that guarantees you regular payments over the lifetime of the Annuities are long term financial annuitant, typically in the form of a check or an automatic deposit made to your bank contracts designed to help secure account. Annuity income can be a welcome supplement to other forms of income in your financial future by providing retirement, such as Social Security payments, retirement plan distributions and earned you with a predictable, guaranteed income—helping you enjoy a more comfortable future. -
Book I. Title XIV. Concerning Statutes, Imperial Constitutions and Edicts. (De Legibus Et Constitutionibus Principum Et Edictis
Book I. Title XIV. Concerning statutes, imperial constitutions and edicts. (De legibus et constitutionibus principum et edictis.) Bas. 2.6.6; D. 1.3.4. Headnote. Sources of the law. During the republic, laws were largely made by popular assemblies which, however, passed out of existence soon after the beginning of the empire. For some time the senate had the power to adopt laws (senatus consulta). But that body, too, gradually lost its power and influence under the empire. Statements (orations) made in the senate, or sent to it, by the emperor, were for some time ratified by it, but this practice ceased in the latter part of the third century, the orations thereafter, whenever made or sent to that body, having the force of law without a vote of confirmation. (Buckland 15.) D. 1.3.9 says that “nobody questions that the senate can make law.” And C. 1.16 confirms that statement. Nevertheless, the right existed theoretically only, since that body was absolutely dependent on the will of the sovereign. C. 1.14.8 shows an enactment of the year 446 A. D. in which the emperor stated that the senate should thereafter be consulted in the enactment of new laws. How far the rule was carried out is not known. Another source of law in the early days was through the edicts of the praetors, the ordinary judges at Rome. These praetors at the beginning of their year of office would issue a general edict stating what principles, aside from the ordinary rules of the civil (common) law, they would observe during their term of office. -
Annuity Options in Public Pension Plans: the Curious Case of Social Security Leveling Robert Clark Robert Hammond Melinda Morrill David Vandeweide
Annuity Options in Public Pension Plans: The Curious Case of Social Security Leveling Robert Clark Robert Hammond Melinda Morrill David Vandeweide 1 Key Questions 1. What is Social Security Leveling? 2. Is SS Leveling a mere curiosity or a widely used annuity option in public retirement plans? 3. Do many retirees choose SS Leveling? 4. How does SS Leveling affect lifetime income? 5. What policy changes would improve this annuity option? 2 What is Social Security Leveling? Public pension plans offer a series of payout options: Lump sum distribution Single life annuities Joint & Survivor annuities Public plans not subject to ERISA J&S annuities are not the default option in most states 3 What is Social Security Leveling? SS Leveling is a single life annuity that front loads payments from the pension Only individuals retiring prior to leveling age are eligible to select leveling Individuals selecting the SS Leveling option are choosing a single life annuity with no survivor benefits 4 Reasons for front loading benefits Desire for consumption smoothing High personal discount rate Possible effects of selecting SS leveling • Reduced likelihood of post-retirement work • Increase likelihood of claiming SS benefits at 62 5 What is Social Security Leveling? Retiring worker must present the pension system an estimate of the SS benefit they are expected to receive at age 62 based on no further work Retirement system determines a benefit (B1) to be paid from time of retirement until age 62 and a benefit that will be paid from age 62 until death (B2) -
Justinian's Redaction
JUSTINIAN'S REDACTION. "Forhim there are no dry husks of doctrine; each is the vital develop- ment of a living germ. There is no single bud or fruit of it but has an ancestry of thousands of years; no topmost twig that does not greet with the sap drawn from -he dark burrows underground; no fibre torn away from it but has been twisted and strained by historic wheels. For him, the Roman law, that masterpiece of national growth, is no sealed book ..... ... but is a reservoir of doctrine, drawn from the watershed of a world's civilization!'* For to-day's student of law, what worth has the half- dozen years' activity of a few Greek-speakers by the Bos- phorus nearly fourteen centuries ago? Chancellor Kent says: "With most of the European nations, and in the new states of Spanish America, and in one of the United States, it (Roman law) constitutes the principal basis of their unwritten or common law. It exerts a very considerable influence on our own municipal law, and particularly on those branches of it which are of equity and admiralty jurisdiction, or fall within the cognizance of the surrogate or consistorial courts . It is now taught and obeyed not only in France, Spain, Germany, Holland, and Scotland, but in the islands of the Indian Ocean, and on the banks of the Mississippi and St. Lawrence. So true, it seems, are the words of d'Agnesseau, that 'the grand destinies of Rome are not yet accomplished; she reigns throughout the world by her reason, after having ceased to reign by her authority?'" And of the honored jurists whose names are carved on the stones of the Law Building of the University of Pennsyl- vania another may be cited as viewing the matter from a different standpoint. -
Optimal Mandates and the Welfare Cost of Asymmetric Information: Evidence from the U.K
Econometrica, Vol. 78, No. 3 (May, 2010), 1031–1092 OPTIMAL MANDATES AND THE WELFARE COST OF ASYMMETRIC INFORMATION: EVIDENCE FROM THE U.K. ANNUITY MARKET BY LIRAN EINAV,AMY FINKELSTEIN, AND PAUL SCHRIMPF1 Much of the extensive empirical literature on insurance markets has focused on whether adverse selection can be detected. Once detected, however, there has been little attempt to quantify its welfare cost or to assess whether and what potential gov- ernment interventions may reduce these costs. To do so, we develop a model of annuity contract choice and estimate it using data from the U.K. annuity market. The model allows for private information about mortality risk as well as heterogeneity in prefer- ences over different contract options. We focus on the choice of length of guarantee among individuals who are required to buy annuities. The results suggest that asym- metric information along the guarantee margin reduces welfare relative to a first-best symmetric information benchmark by about £127 million per year or about 2 percent of annuitized wealth. We also find that by requiring that individuals choose the longest guarantee period allowed, mandates could achieve the first-best allocation. However, we estimate that other mandated guarantee lengths would have detrimental effects on welfare. Since determining the optimal mandate is empirically difficult, our findings suggest that achieving welfare gains through mandatory social insurance may be harder in practice than simple theory may suggest. KEYWORDS: Annuities, contract choice, adverse selection, structural estimation. 1. INTRODUCTION EVER SINCE THE SEMINAL WORKS of Akerlof (1970) and Rothschild and Stiglitz (1976), a rich theoretical literature has emphasized the negative wel- fare consequences of adverse selection in insurance markets and the potential for welfare-improving government intervention. -
Retirement Income/Annuities Around the World What US Policy Makers Might Learn
May 2009 Retirement Income/Annuities Around the World What US Policy Makers Might Learn Barbara Marder, Baltimore Global Defined Contribution Consulting Leader www.mercer.com 1 Comparison of annuity markets (OECD National Annuity Markets: Features and Implications, Rusconi 2008) Mercer 1 2 Retirement Income Across Europe – Diverse Approach DC types in EU Member States Euro, Guarantees, Annuities, Investment Choices, Prevalence United Kingdom (UK) Czech Republic (CZ) Luxembourg (LU) Netherlands (NL) Denmark (DK) (DE) Germany Romania (RO) Lithuania (LT) Hungary (HU) Bulgaria (BG) Bulgaria Slovakia (SK) Slovakia Portugal (PT) Belgium (BE) Sweden (SE) Sweden Slovenia (SI) Estonia (EE) Cyprus (CY) Austria (AT) Greece (EL) Greece France (FR) Poland (PL) Finland (FI) Ireland (IE) Ireland Latvia (LV) Spain (ES) Malta (MT) Italy (IT) Italy Type Euro zone ● = Y ● = N ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Guaranteed returns ● = N ● = Y ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● = Mixture Annuity required ● = N ● = Y ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● = Choice Member investment choice ● = Y ● = N ● = Lifecycle ○ ● ● ○ ● ○ ● ● ○ ● ● ● ● ● ● ● ● ○ ● ○ = Rare ○ = Some ○ = Mixture DC prevalence ● = High ● = Low ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● = Medium Mercer 0 Mercer 2 3 Australia •Programmed withdrawal/allocated income stream is most popular retirement income option •Retiree account increases with investment earnings, can vary annual income received •2007 simplification to remove taxation for persons age 60 +, lump sum and pensions -
Part I. the Legacy of Roman Law
Sec. iA JUSTINIAN’S INSTITUTES I–1 PART I. THE LEGACY OF ROMAN LAW A. JUSTINIAN’S INSTITUTES Contents, Proemium, 1.1–3, 1.8pr, 1.9–10, 2.1–2, 2.5.6, 2.9.6, 3.13, 4.1pr, 4.6.pr–30 J.B. Moyle trans. (Oxford, 1913) [Some emendations by CD.]1 CONTENTS) PROOEMIUM Book I. Title I. Of Justice and Law II. Of the law of nature, the law of nations, and the civil law III. Of the law of persons IV. Of men free born V. Of freedmen VI. Of persons unable to manumit, and the causes of their incapacity VII. Of the repeal of the lex Fufia Caninia VIII. Of persons independent or dependent XI. Of paternal power X. Of marriage XI. Of adoptions XII. Of the modes in which paternal power is extinguished XIII. Of guardianships XIV. Who can be appointed guardians by will XV. Of the statutory guardianship of agnates XVI. Of loss of status XVII. Of the statutory guardianship of patrons XVIII. Of the statutory guardianship of parents XIX. Of fiduciary guardianship XX. Of Atilian guardians, and those appointed under the lex Iulia et Titia XXI. Of the authority of guardians XXII. Of the modes in which guardianship is terminated XXIII. Of curators XXIV. Of the security to be given by guardians and curators XXV. Of guardians’ and curators’ grounds of exemption XXVI. Of guardians or curators who are suspected BOOK II. Title I. Of the different kinds of Things II. Of incorporeal Things III. Of servitudes IV. Of usufruct V. -
A Corpus Approach to Roman Law Based on Justinian's Digest
informatics Article A Corpus Approach to Roman Law Based on Justinian’s Digest Marton Ribary 1,* and Barbara McGillivray 2,3 1 School of Law, University of Surrey, Guildford GU2 7XH, UK 2 Theoretical and Applied Linguistics, Faculty of Modern and Medieval Languages and Linguistics, University of Cambridge, Cambridge CB3 9DA, UK; [email protected] 3 The Alan Turing Institute, London NW1 2DB, UK * Correspondence: [email protected] Received: 21 September 2020; Accepted: 13 October 2020; Published: 15 October 2020 Abstract: Traditional philological methods in Roman legal scholarship such as close reading and strict juristic reasoning have analysed law in extraordinary detail. Such methods, however, have paid less attention to the empirical characteristics of legal texts and occasionally projected an abstract framework onto the sources. The paper presents a series of computer-assisted methods to open new frontiers of inquiry. Using a Python coding environment, we have built a relational database of the Latin text of the Digest, a historical sourcebook of Roman law compiled under the order of Emperor Justinian in 533 CE. Subsequently, we investigated the structure of Roman law by automatically clustering the sections of the Digest according to their linguistic profile. Finally, we explored the characteristics of Roman legal language according to the principles and methods of computational distributional semantics. Our research has discovered an empirical structure of Roman law which arises from the sources themselves and complements the dominant scholarly assumption that Roman law rests on abstract structures. By building and comparing Latin word embeddings models, we were also able to detect a semantic split in words with general and legal sense.