Value Of Annuity Research Articles

Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

Economic Effects Real Estate Tax

Summary The real estate tax is usually a fiscal instrument which performs the property tax. When it comes to real property or immovable this term include: apartments, houses, land, cottages, excess housing landscape and more. The real estate tax as a form of the fiscal charges ownership or use of certain forms of real estate, and the revenue from this tax is levied on the area where the property is located regardless of the place of residence of its owner. The tax base for the calculation of this tax usually consists of the market, estimated or annuity value of certain real estate. This form of taxation in the Republic of Serbian applies from 1.1.2012., and its introduction has been replaced by former property taxes. The differences between the two concepts mentioned taxes are numerous and significant. Among the more important are: subject to taxation under the new concept of the real estate rather than law, a taxpayer is any property owner rather than the holder of rights to immovable property tax base is the market value of real estate which is replaced by the payment of taxes per square meter of usable area, the rate of property tax is determined local government, which can not be lower than 0.05% of the estimated value of the real estate nor higher than 0.5% of the appraised value of real estate. The last change, ie. The new law on Property Tax from 5.11.2015. was determined by the tax rate to 20%. The fact that local governments each of them determines the tax rate on real estate which range from high to low rates of multiple, makes this tax is progressive. Progression is particularly expressed in the distinction applied tax rates of developed and undeveloped municipalities, where we have a case that less developed tolerate a higher tax burden, which leads to negative economic effects. However, real estate tax has its own economic and social characteristics which must be aligned with the objectives of tax policy. This means that the real estate tax should be considered from the standpoint of the entire tax system and not from the standpoint of individual income tax forms.

Modeling and Forecasting Mortality Using the Lee-Carter Model for Indian Population Based on Decade-wise Data

The stochastic mortality model given by Lee and Carter (1992) has been used in literature for fitting and forecasting the human mortality. We have modeled mortality rates of Indian population using the Lee-Carter (LC) model based on decade-wise data available separately for Indian female and male populations in the form of life tables for the period 1901-2011. The Singular Value Decomposition (SVD) approach is used for estimation of the parameters of the LC model. Forecasted values of time dependent parameter of the LC model are obtained for next five decades using best fitted auto regressive integrated moving average (ARIMA) model. Forecasted values of life expectancy at different ages with 95% confidence intervals are also reported for the next five decades. As an application, using forecasted mortality rates for the next five decades, net single premium for whole life and term insurance, actuarial present values of life annuities for some selected ages are also evaluated

A Paradox Within The Time Value Of Money: A Critical Thinking Exercise For Finance Students

This study presents a paradox within the time value of money (TVM), namely, that the interest-principal sequence embedded in the payment stream of an amortized loan is exactly the opposite of the interest-principal sequence implicit in the present value of a matching annuity. We examine this inverse sequence, both mathematically and intuitively, and argue that it provides an excellent exercise for finance students to explore, both to enhance their critical thinking skills as well as to strengthen their understanding of TVM concepts. Additionally, such an exercise will involve them actively in the learning process, as mandated by AACSB International’s Eligibility Procedures and Standards for Business Accreditation.

PENENTUAN CADANGAN PREMI UNTUK ASURANSI JOINT LIFE

Premium reserve is a number of fund that need to be raised by insurance company in preparation for the payment of claims. This study aims to get the formula of premium reserve as well as the value of the premium reserve for joint life insurance by using retrospective calculation method. Joint life insurance participants in this study are limited to 2 people. Calculations in this study is using Indonesian Mortality Table (TMI) 2011, joint life mortality tables, commutation tables, value of annuities, value of single premiums and constant annual premium and using constant interest rates of 5%. The results showed that by using age of the participant insurance joint life of x = 50 and y = 45 years and the premium payment period of t = 10 years, we obtained that the value of premium reserve from the end of the first year until the end of the 11th year has increased every year, while the value of premium reserves from the end of the 12th year and so on until a lifetime has decreased every year.

Phantoms Never Die: Living with Unreliable Population Data

SummaryThe analysis of national mortality trends is critically dependent on the quality of the population, exposures and deaths data that underpin death rates. We develop a framework that allows us to assess data reliability and to identify anomalies, illustrated, by way of example, using England and Wales population data. First, we propose a set of graphical diagnostics that help to pinpoint anomalies. Second, we develop a simple Bayesian model that allows us to quantify objectively the size of any anomalies. Two-dimensional graphical diagnostics and modelling techniques are shown to improve significantly our ability to identify and quantify anomalies. An important conclusion is that significant anomalies in population data can often be linked to uneven patterns of births of people in cohorts born in the distant past. In the case of England and Wales, errors of more than 9% in the estimated size of some birth cohorts can be attributed to an uneven pattern of births. We propose methods that can use births data to improve estimates of the underlying population exposures. Finally, we consider the effect of anomalies on mortality forecasts and annuity values, and we find significant effects for some cohorts. Our methodology has general applicability to other sources of population data, such as the Human Mortality Database.

Estimating the joint survival probabilities of married individuals

We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared polynomials. Also based on a nonparametric comparison, we find that extending the independent Weibull distribution by a squared third order polynomial shows the best performance. We illustrate our model by calculating remaining life expectancies and annuity values. We find that the husbands life expectancy at birth is generally increasing with his wifes age of death and the wifes life expectancy at birth is generally increasing with her husbands age of death. Ignoring the dependence between the remaining lifetimes of spouses may lead to an underestimation of the value of a joint annuity and an overestimation of the value of a single-life annuity, but less than suggested on the basis of the previous literature.

MENENTUKAN PREMI TAHUNAN UNTUK TIGA ORANG PADA ASURANSI JIWA HIDUP GABUNGAN (JOINT LIFE)

Life insurance products consist of a single life insurance and joint life insurance. Joint life is a state where the rule die life is a combination of two or more factors, such as the husband-wife, parent-child. The research is to obtain the formula of the annual premium of joint life insurance with the age of x, y, and z. By using formula and constants Helligmann-Pollard will be determined value of mortality tables, life annuity and single premium to get the formula annual premium joint life insurance for three persons. In addition, this study also aims to get the number of annual premium joint life insurance for a household of three consisting of a married couple and one son with the ages of 50, 45, dan 15 years old, with the interest rate of 5% used. For the contract terms of one and two years, the annual premium of joint life for two persons respectively and greater than the joint life insurance of three persons. While for three to ten years contract, the annual premium of joint life insurance three person is bigger than the joint life insurance for two persons.

MENENTUKAN FORMULA PREMI TAHUNAN TIDAK KONSTAN PADA ASURANSI JOINT LIFE

The aim of this research was to determine the annual premium formula that turns on the joint life insurance. This formula uses the reference insurance contracts of the previous research Insurance Models for Joint Life and Last Survivor Benefits. The first step is to determine the value of mortality tables by using the Table Helligman-pollard. Furthermore, determining the value of a life annuity and single premium. The results of this research was formula to be affected by the changing premium () with the increase and decrease in constant interest.

A Quick Approximation for Modified Bond Duration and Convexity

A bond pricing formula introduced by Arnold [2014] and Arnold and Earl [2014] is used as the basis for calculating bond duration and convexity. By calculating a present value annuity using the coupon rate as the discount rate, approximations for bond duration and convexity emerge that are much less calculation intensive and are reasonably accurate.

Optimal Annuity Purchases for Australian Retirees

We develop and simulate a stochastic lifecycle model to investigate optimal annuity purchases at retirement. Retirees can invest in risky assets, purchase fairly priced immediate or deferred lifetime annuities, and are eligible for a targeted safety net pension. We match baseline parameters to current Australian settings and conduct scenario analyses over a wide range of individual preferences and financial market outcomes. Except where individuals need to insure a consumption floor, both immediate and deferred annuity purchases are largely crowded out by the means‐tested public pension. Welfare losses caused by zero annuitisation are small compared with the losses caused by completely annuitising all savings, particularly if wealth at retirement is low. Decumulation policy should ensure individuals are well informed of the insurance value of annuities and accommodate diverse choices.

Does the St. Petersburg Paradox Cast Doubt on the Use of Expected Value Theory to Approximate the Random Present Value of a Life Annuity?

The classic approximation of the random present value (PV) of a life annuity is its expected PV (EPV) over its term. EPV minimizes mean squared error per expected value theory (EVT). Here, based on the experimental work of Hayden and Platt (2009), lessons are drawn from the St. Petersburg paradox (SPP) which violates EVT, to improve random PV approximations. Although much work over the last 300 years has been done to try and resolve the SPP, the question of whether it offers lessons for approximating any random PV has not been considered in the literature. An additional approximation, the median PV (PV*), which has minimal mean absolute error, is introduced herein. PV* can yield a probability (k) greater than 50% that its absolute error is less than the absolute error in EPV. If k is revealed, would agents value the annuity in terms of its EPV and, thus, willingly allow crosssubsidization to dominate their self-interest to only pay amounts that are reasonably commensurate with the PV of the payouts they hope to get in return? It is proposed that the value of the annuity when approximated as the weighted average of PV* and EPV, with k and 1 – k as weights, respectively, makes cross-subsidization of annuitants fairer in the sense of Rawls (1971) and Sen (1992).

Cohort and target age effects on subjective survival probabilities: Implications for models of the retirement phase

Subjective survival scaling factors are often estimated from one observation of life expectancy and treated as constant to any target age. Using new survey data on subjective survival probabilities, we estimate a model incorporating cohort- and target age-varying beliefs in scaling factors. Both cohort age and target age matter: respondents are pessimistic about overall life expectancy but optimistic about survival at advanced ages, and older respondents are more optimistic than younger. We propose a new theoretical model incorporating cohort- and target age-varying beliefs and illustrate their effects on the perceived value of annuities and on retirement phase consumption plans.

Оценивание актуарной современной стоимости полной непрерывной пожизненной ренты

Оценивание актуарной современной стоимости полной непрерывной пожизненной ренты

PENENTUAN CADANGAN PREMI UNTUK ASURANSI PENDIDIKAN

This aims of this research is determine the insurance premium reserve for education with retrospective calculations and determine the premium reserves who acquired during the period of guarantee for insurance education. This research observes the premium reserve for persons aged 40 years with a coverage period of 17 years. The secondary data used is an education insurance data product from the insurance company that issued the insurance product. Premium reserve is determined by using the retrospective calculation, the calculation using the annuity value, net single premium value, net annual premiums, the value of net monthly premium, CSO 1980 mortality and fixed interest rate at 9%. Retrospective calculations produce a faster value backup and sequentially in each year. The results showed that the premium reserve with retrospective calculation should be close up to the cash price owned by insurance company and must be the same at the end of the insurance period is Rp 7.000.000,00.

Phantoms Never Die: Living with Unreliable Population Data

The analysis of national mortality trends is critically dependent on the quality of the population, exposures and deaths data that underpin death rates.We develop a framework that allows us to assess data reliability and to identify anomalies, illustrated, by way of example, using England and Wales population data. First, we propose a set of graphical diagnostics that help to pinpoint anomalies. Second, we develop a simple Bayesian model that allows us to quantify objectively the size of any anomalies. Two-dimensional graphical diagnostics and modelling techniques are shown to improve significantly our ability to identify and quantify anomalies. An important conclusion is that significant anomalies in population data can often be linked to uneven patterns of births of people in cohorts born in the distant past. In the case of England and Wales, errors of more than 9% in the estimated size of some birth cohorts can be attributed to an uneven pattern of births.We propose methods that can use births data to improve estimates of the underlying population exposures. Finally, we consider the effect of anomalies on mortality forecasts and annuity values, and we find significant effects for some cohorts. Our methodology has general applicability to other sources of population data, such as the Human Mortality Database.

Beyond Age and Sex: Enhancing Annuity Pricing

This paper examines the use of more extensive risk classification and its impact on annuitisation values in consumer markets with mortality heterogeneity. Prices of U.S. retail annuities do not currently reflect buyers’ attributes other than age and sex. I qualitatively assess a number of proposed underwriting factors and show that the factors chosen can robustly predict mortality heterogeneity in a hazards framework. The relative value of annuities across demographic groups converges considerably under finer-grained pricing, but the change in consumers’ well-being is asymmetric. Shorter-lived annuitants gain about 30 per cent in financial and utility-adjusted terms, whereas longer-lived annuitants experience losses of 16 per cent.

Risk aggregation and stochastic claims reserving in disability insurance

We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic–demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving and risk aggregation for large portfolios. Further, we derive a partial differential equation for moments of present values. Moreover, we show how statistical multi-factor intensity models can be approximated by one-factor models, which allows for solving the PDEs very efficiently. Finally, we give a numerical example where moments of present values of disability annuities are computed using finite-difference methods and Monte Carlo simulations.

Optimal Annuity Purchases for Australian Retirees

We develop and simulate a stochastic lifecycle model to investigate optimal annuity purchases at retirement. Retirees can invest in risky assets, purchase fairly priced immediate or deferred lifetime annuities, and are eligible for a targeted safety net pension. We match baseline parameters to current Australian settings and conduct scenario analyses over a wide range of individual preferences and financial market outcomes. Except where individuals need to insure a consumption floor, both immediate and deferred annuity purchases are largely crowded out by the means‐tested public pension. Welfare losses caused by zero annuitisation are small compared with the losses caused by completely annuitising all savings, particularly if wealth at retirement is low. Decumulation policy should ensure individuals are well informed of the insurance value of annuities and accommodate diverse choices.

Mortality Improvements -- The Case of South Africa

We remedy the lack of quantified mortality improvement information for South Africa by deriving forecasts of the mortality trend based on the South African experience for the years 1996-2011 using the Lee-Carter (1985) and Cairns-Blake-Dowd (2006) models. We utilize a public health perspective to provide context to the modelled forecasts. Conversely, we discuss the possible benefits to public health policy provided by actuarial forecasts of mortality trends. Our results, which indicate a decreasing mortality trend for the geriatric population, are used to illustrate a range of annuity values and comment on the industry use of the PA(90) table. Lastly, we discuss possible implications of our forecast for future public health decision making and point the way to future research.