Ruin Problem in Retirement Under Stochastic Return Rate and Mortality Rate and Its Applications PDF Download
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Author: Feng Li Publisher: ISBN: Category : Insurance Languages : en Pages : 120
Book Description
Retirees face a difficult choice between annuitization from insurance firms and self-management or so-called self-annuitization. Self-annuitization could provide a higher consumption by investing more assets on equity market but with a risk that retirees may outlive the income from their self-managed assets. Using the Ornstein-Uhlenbeck stochastic model, also called the Vasicek model, for the rate of return, we focus our study on the ruin probability in retirement. We show how asset mix, initial rate of return, and gender impact the ruin probability in retirement. We derive a recursive formula to calculate an approximate distribution for the present value of the life annuity function under our stochastic model. Finally, we use our model to illustrate how a VaR technique can help determine the optimal consumption for a retiree with a certain tolerance to ruin under different retirement goals.
Author: Feng Li Publisher: ISBN: Category : Insurance Languages : en Pages : 120
Book Description
Retirees face a difficult choice between annuitization from insurance firms and self-management or so-called self-annuitization. Self-annuitization could provide a higher consumption by investing more assets on equity market but with a risk that retirees may outlive the income from their self-managed assets. Using the Ornstein-Uhlenbeck stochastic model, also called the Vasicek model, for the rate of return, we focus our study on the ruin probability in retirement. We show how asset mix, initial rate of return, and gender impact the ruin probability in retirement. We derive a recursive formula to calculate an approximate distribution for the present value of the life annuity function under our stochastic model. Finally, we use our model to illustrate how a VaR technique can help determine the optimal consumption for a retiree with a certain tolerance to ruin under different retirement goals.
Author: Patrick J. Collins Publisher: CFA Institute Research Foundation ISBN: 193466796X Category : Business & Economics Languages : en Pages : 106
Book Description
The past 50 years have seen an abundance of research on retirement planning and longevity risk. Reviewed here is the academic side of the research and its varied viewpoints and nuances. The evolution of retirement risk models, retirement portfolio problems and solutions, and annuities are some of the many topics covered.
Author: Salvatore Federico Publisher: ISBN: 9783039360581 Category : Languages : en Pages : 206
Book Description
In a world dominated by uncertainty, modeling and understanding the optimal behavior of agents is of the utmost importance. Many problems in economics, finance, and actuarial science naturally require decision makers to undertake choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and risk, hedging, optimal timing issues in pricing American options, and investment decisions. Stochastic control theory provides the methods and results to tackle all such problems. This book is a collection of the papers published in the Special Issue "Applications of Stochastic Optimal Control to Economics and Finance", which appeared in the open access journal Risks in 2019. It contains seven peer-reviewed papers dealing with stochastic control models motivated by important questions in economics and finance. Each model is rigorously mathematically funded and treated, and the numerical methods are employed to derive the optimal solution. The topics of the book's chapters range from optimal public debt management to optimal reinsurance, real options in energy markets, and optimal portfolio choice in partial and complete information settings. From a mathematical point of view, techniques and arguments of dynamic programming theory, filtering theory, optimal stopping, one-dimensional diffusions and multi-dimensional jump processes are used.
Author: Moshe A. Milevsky Publisher: Cambridge University Press ISBN: 1139454862 Category : Business & Economics Languages : en Pages : 301
Book Description
This 2006 book introduces and develops the basic actuarial models and underlying pricing of life-contingent pension annuities and life insurance from a unique financial perspective. The ideas and techniques are then applied to the real-world problem of generating sustainable retirement income towards the end of the human life-cycle. The role of lifetime income, longevity insurance, and systematic withdrawal plans are investigated in a parsimonious framework. The underlying technology and terminology of the book are based on continuous-time financial economics by merging analytic laws of mortality with the dynamics of equity markets and interest rates. Nonetheless, the book requires a minimal background in mathematics and emphasizes applications and examples more than proofs and theorems. It can serve as an ideal textbook for an applied course on wealth management and retirement planning in addition to being a reference for quantitatively-inclined financial planners.
Author: S. David Promislow Publisher: John Wiley & Sons ISBN: 0470978074 Category : Mathematics Languages : en Pages : 390
Book Description
This book provides a comprehensive introduction to actuarial mathematics, covering both deterministic and stochastic models of life contingencies, as well as more advanced topics such as risk theory, credibility theory and multi-state models. This new edition includes additional material on credibility theory, continuous time multi-state models, more complex types of contingent insurances, flexible contracts such as universal life, the risk measures VaR and TVaR. Key Features: Covers much of the syllabus material on the modeling examinations of the Society of Actuaries, Canadian Institute of Actuaries and the Casualty Actuarial Society. (SOA-CIA exams MLC and C, CSA exams 3L and 4.) Extensively revised and updated with new material. Orders the topics specifically to facilitate learning. Provides a streamlined approach to actuarial notation. Employs modern computational methods. Contains a variety of exercises, both computational and theoretical, together with answers, enabling use for self-study. An ideal text for students planning for a professional career as actuaries, providing a solid preparation for the modeling examinations of the major North American actuarial associations. Furthermore, this book is highly suitable reference for those wanting a sound introduction to the subject, and for those working in insurance, annuities and pensions.
Author: Moshe Arye Milevsky Publisher: Springer Nature ISBN: 303051434X Category : Business & Economics Languages : en Pages : 302
Book Description
This book provides computational tools that readers can use to flourish in the retirement income industry. Each chapter describes recipe-like algorithms and explains how to implement them via simple scripts in the freely available R coding language. Students can use those skills to generate quantitative answers to the most common questions in retirement income planning, as well as to develop a deeper understanding of the finance and economics underlying the field itself. The book will be an excellent asset for experienced students who are interested in advanced wealth management, and specifically within courses that focus on holistic modeling of the retirement income process. The material will also be useful to current and future wealth management professionals within the financial services industry. Readers should have a solid understanding of financial principles, as well as a rudimentary background in economics and accounting.
Author: Feng Li
Author: Feng Li
Author: Jinlian Wang
Author: Patrick J. Collins
Author: Salvatore Federico
Author: D.R. Cox
Author: Larry Heligman
Author: Moshe A. Milevsky
Author: 
Author: S. David Promislow
Author: Moshe Arye Milevsky