Stochastic Mortality Models with Applications in Financial Risk Management
Author : Siu Hang Li
Publisher :
Page : pages
File Size : 48,55 MB
Release : 2007
Category :
ISBN :
Integrating Financial and Demographic Longevity Risk Models
Author : Michael Sherris
Publisher :
Page : 0 pages
File Size : 41,64 MB
Release : 2011
Category :
ISBN :
Book Description
Since its introduction, the Lee Carter model has been widely adopted as a means of modelling the distribution of projected mortality rates. Increasingly attention is being placed on alternative models and, importantly in the financial and actuarial literature, on models suited to risk management and pricing. Financial economic approaches based on term structure models provide a framework for embedding longevity models into a pricing and risk management framework. They can include traditional actuarial models for the force of mortality as well as multiple risk factor models. The paper develops a stochastic longevity model suitable for financial pricing and risk management applications based on Australian population mortality rates from 1971-2004 for ages 50-99. The model allows for expected changes arising from age and cohort effects and includes multiple stochastic risk factors. The model captures age and time effects and allows for age dependence in the stochastic factors driving longevity improvements. The model provides a good fit to historical data capturing the stochastic trends in mortality improvement at different ages and across time as well as the multivariate dependence structure across ages.
Stochastic Mortality Modelling
Author : Xiaoming Liu
Publisher :
Page : 380 pages
File Size : 38,99 MB
Release : 2008
Category :
ISBN : 9780494590171
Book Description
For life insurance and annuity products whose payoffs depend on the future mortality rates, there is a risk that realized mortality rates will be different from the anticipated rates accounted for in their pricing and reserving calculations. This is termed as mortality risk. Since mortality risk is difficult to diversify and has significant financial impacts on insurance policies and pension plans, it is now a well-accepted fact that stochastic approaches shall be adopted to model the mortality risk and to evaluate the mortality-linked securities.To be more specific, we consider a finite-state Markov process with one absorbing state. This Markov process is related to an underlying aging mechanism and the survival time is viewed as the time until absorption. The resulting distribution for the survival time is a so-called phase-type distribution. This approach is different from the traditional curve fitting mortality models in the sense that the survival probabilities are now linked with an underlying Markov aging process. Markov mathematical and phase-type distribution theories therefore provide us a flexible and tractable framework to model the mortality dynamics. And the time-changed Markov process allows us to incorporate the uncertainties embedded in the future mortality evolution.The proposed model has been applied to price the EIB/BNP Longevity Bonds and other mortality derivatives under the independent assumption of interest rate and mortality rate. A calibrating method for the model is suggested so that it can utilize both the market price information involving the relevant mortality risk and the latest mortality projection. The proposed model has also been fitted to various type of population mortality data for empirical study. The fitting results show that our model can interpret the stylized mortality patterns very well.The objective of this thesis is to propose the use of a time-changed Markov process to describe stochastic mortality dynamics for pricing and risk management purposes. Analytical and empirical properties of this dynamics have been investigated using a matrix-analytic methodology. Applications of the proposed model in the evaluation of fair values for mortality linked securities have also been explored.
Stochastic Mortality Modelling
Author : Xiaoming Jr Liu
Publisher :
Page : pages
File Size : 27,61 MB
Release :
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ISBN :
Book Description
Actuarial Finance
Author : Mathieu Boudreault
Publisher : John Wiley & Sons
Page : 853 pages
File Size : 22,42 MB
Release : 2019-04-01
Category : Mathematics
ISBN : 1119137020
Book Description
A new textbook offering a comprehensive introduction to models and techniques for the emerging field of actuarial Finance Drs. Boudreault and Renaud answer the need for a clear, application-oriented guide to the growing field of actuarial finance with this volume, which focuses on the mathematical models and techniques used in actuarial finance for the pricing and hedging of actuarial liabilities exposed to financial markets and other contingencies. With roots in modern financial mathematics, actuarial finance presents unique challenges due to the long-term nature of insurance liabilities, the presence of mortality or other contingencies and the structure and regulations of the insurance and pension markets. Motivated, designed and written for and by actuaries, this book puts actuarial applications at the forefront in addition to balancing mathematics and finance at an adequate level to actuarial undergraduates. While the classical theory of financial mathematics is discussed, the authors provide a thorough grounding in such crucial topics as recognizing embedded options in actuarial liabilities, adequately quantifying and pricing liabilities, and using derivatives and other assets to manage actuarial and financial risks. Actuarial applications are emphasized and illustrated with about 300 examples and 200 exercises. The book also comprises end-of-chapter point-form summaries to help the reader review the most important concepts. Additional topics and features include: Compares pricing in insurance and financial markets Discusses event-triggered derivatives such as weather, catastrophe and longevity derivatives and how they can be used for risk management; Introduces equity-linked insurance and annuities (EIAs, VAs), relates them to common derivatives and how to manage mortality for these products Introduces pricing and replication in incomplete markets and analyze the impact of market incompleteness on insurance and risk management; Presents immunization techniques alongside Greeks-based hedging; Covers in detail how to delta-gamma/rho/vega hedge a liability and how to rebalance periodically a hedging portfolio. This text will prove itself a firm foundation for undergraduate courses in financial mathematics or economics, actuarial mathematics or derivative markets. It is also highly applicable to current and future actuaries preparing for the exams or actuary professionals looking for a valuable addition to their reference shelf. As of 2019, the book covers significant parts of the Society of Actuaries’ Exams FM, IFM and QFI Core, and the Casualty Actuarial Society’s Exams 2 and 3F. It is assumed the reader has basic skills in calculus (differentiation and integration of functions), probability (at the level of the Society of Actuaries’ Exam P), interest theory (time value of money) and, ideally, a basic understanding of elementary stochastic processes such as random walks.
A Multivariate Forward-Rate Mortality Framework
Author : Daniel H. Alai
Publisher :
Page : 0 pages
File Size : 27,75 MB
Release : 2015
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ISBN :
Book Description
Stochastic mortality models have been developed for a range of applications from demographic projections to financial management. Financial risk based models build on methods used for interest rates and apply these to mortality rates. They have the advantage of being applied to financial pricing and the management of longevity risk. Olivier and Jeffery (2004) and Smith (2005) proposed a model based on a forward-rate mortality framework with stochastic factors driven by univariate gamma random variables irrespective of age or duration. We assess and further develop this model. We generalize random shocks from a univariate gamma to a univariate Tweedie distribution and allow for the distributions to vary by age. Furthermore, since dependence between ages is an observed characteristic of mortality rate improvements, we formulate a multivariate framework using copulas. We find that dependence increases with age and introduce a suitable covariance structure, one that is related to the notion of a minimum. The resulting model provides a more realistic basis for capturing the risk of mortality improvements and serves to enhance longevity risk management for pension and insurance funds.
Mortality Risk Modeling
Author : Samuel H. Cox
Publisher :
Page : 35 pages
File Size : 34,15 MB
Release : 2011
Category :
ISBN :
Book Description
This paper proposes a stochastic mortality model featuring both permanent longevity jump and temporary mortality jump processes. A trend reduction component describes unexpected mortality improvement over an extended period of time. The model also captures the uneven effect of mortality events on different ages and the correlations among them. The model will be useful in analyzing future mortality dependent cash flows of life insurance portfolios, annuity portfolios, and portfolios of mortality derivatives. We show how to apply the model to analyze and price a longevity security.
Stochastic Systematic Mortality Risk Modeling Under Collateral Data and Actuarial Applications
Author : Joab Onyango Odhiambo
Publisher : Eliva Press
Page : 0 pages
File Size : 29,48 MB
Release : 2023-03-26
Category :
ISBN : 9789994987313
Book Description
Many actuaries worldwide use Systematic Mortality Risk (SMR) to value actuarial products such as annuities and assurances sold to policyholders. Data availability plays an essential role in ascertaining the SMR models' accuracy, and it varies from one country to another. Incorrect stochastic modeling of SMR models due to paucity of data has been a problem for many Sub-Saharan African countries such as Kenya, thus prompting modifications of the classical SMR models used in those countries with limited data availability. This study aimed at modelling SMR stochastically under the collateral data environment such as Sub-Saharan African countries like Kenya and then apply it in the current actuarial valuations. This book has formulated novel stochastic mortality risk models under the collateral data setup. Kenya population data is preferably integrated into the commonly applied stochastic mortality risk models under a 3-factor unitary framework of age-time-cohort. After testing SMR models on the Kenyan data to assess their behaviours, we incorporate the Bühlmann Credibility Approach with random coefficients in modeling. The randomness of the classical SMR models was modeled as NIG distribution instead of Normal distribution due to data paucity in Kenya (use of collateral data environment). The Deep Neural Network (DNN) technique solved data paucity during the SMR model fitting and forecasting. The forecasting performances of the SMR models were done under DNN and, compared with those from conventional models, show powerful empirical illustrations in their precision levels. Numerical results showed that SMR models become more accurate under collateral data after incorporating the BCA with NIG assumptions. The Actuarial valuation of annuities and assurances using the new SMR offered much more accurate valuations when compared to those under classical models. The study's findings should help regulators such as IRA and RBA make policy documents that protect all stakeholders in Kenya's insurance, social protection firms, and pension sectors.
Stochastic Mortality Modelling and Management of Longevity Risk with Pricing and Reserving Applications to Annuity Products
Author : Daniel Steuten
Publisher :
Page : 291 pages
File Size : 48,40 MB
Release : 2012
Category :
ISBN :
Book Description
Markovian Approaches to Joint-life Mortality with Applications in Risk Management
Author : Min Ji
Publisher :
Page : 141 pages
File Size : 49,28 MB
Release : 2011
Category :
ISBN :
Book Description
The combined survival status of the insured lives is a critical problem when pricing and reserving insurance products with more than one life. Our preliminary experience examination of bivariate annuity data from a large Canadian insurance company shows that the relative risk of mortality for an individual increases after the loss of his/her spouse, and that the increase is especially dramatic shortly after bereavement. This preliminary result is supported by the empirical studies over the past 50 years, which suggest dependence between a husband and wife. The dependence between a married couple may be significant in risk management of joint-life policies. This dissertation progressively explores Markovian models in pricing and risk management of joint-life policies, illuminating their advantages in dependent modeling of joint time-until-death (or other exit time) random variables. This dissertation argues that in the dependent modeling of joint-life dependence, Markovian models are flexible, transparent, and easily extended. Multiple state models have been widely used in historic data analysis, particularly in the modeling of failures that have event-related dependence. This dissertation introduces a ¡°common shock¡± factor into a standard Markov joint-life mortality model, and then extends it to a semi-Markov model to capture the decaying effect of the "broken heart" factor. The proposed models transparently and intuitively measure the extent of three types of dependence: the instantaneous dependence, the short-term impact of bereavement, and the long-term association between lifetimes. Some copula-based dependence measures, such as upper tail dependence, can also be derived from Markovian approaches. Very often, death is not the only mode of decrement. Entry into long-term care and voluntary prepayment, for instance, can affect reverse mortgage terminations. The semi-Markov joint-life model is extended to incorporate more exit modes, to model joint-life reverse mortgage termination speed. The event-triggered dependence between a husband and wife is modeled. For example, one spouse's death increases the survivor's inclination to move close to kin. We apply the proposed model specifically to develop the valuation formulas for roll-up mortgages in the UK and Home Equity Conversion Mortgages in the US. We test the significance of each termination mode and then use the model to investigate the mortgage insurance premiums levied on Home Equity Conversion Mortgage borrowers. Finally, this thesis extends the semi-Markov joint-life mortality model to having stochastic transition intensities, for modeling joint-life longevity risk in last-survivor annuities. We propose a natural extension of Gompertz' law to have correlated stochastic dynamics for its two parameters, and incorporate it into the semi-Markov joint-life mortality model. Based on this preliminary joint-life longevity model, we examine the impact of mortality improvement on the cost of a last survivor annuity, and investigate the market prices of longevity risk in last survivor annuities using risk-neutral pricing theory.
