scholarly journals LESS-EXPENSIVE VALUATION AND RESERVING OF LONG-DATED VARIABLE ANNUITIES WHEN INTEREST RATES AND MORTALITY RATES ARE STOCHASTIC

2020 ◽  
Vol 50 (2) ◽  
pp. 381-417
Author(s):  
Kevin Fergusson
Keyword(s):  
Interest Rates ◽  
Mortality Rates ◽  
Bessel Process ◽  
Insurance Markets ◽  
Rate Model ◽  
Ancillary Benefits ◽  
Variable Annuities ◽  
Mortality Model ◽  
Squared Bessel Process ◽  
Benchmark Approach

AbstractVariable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing for dependence between financial and insurance markets. Under a simplified case of independence, the results show that when the discounted index is modelled as a time-transformed squared Bessel process, less-expensive valuation and reserving is achieved regardless of the short rate model or the mortality model.

Invariance formulas for stopping times of squared Bessel process

2018 ◽  
Vol 36 (4) ◽  
pp. 671-699
Author(s):  
Jacek Jakubowski ◽  
Maciej Wiśniewolski
Keyword(s):  
Bessel Process ◽  
Stopping Times ◽  
Squared Bessel Process

scholarly journals An Individual-Tree Mortality Model for Complex Stands of Southeastern British Columbia

2005 ◽  
Vol 20 (2) ◽  
pp. 101-109 ◽  
Author(s):  
Hailemariam Temesgen ◽  
Stephen J. Mitchell
Keyword(s):  
British Columbia ◽  
Tree Species ◽  
Tree Mortality ◽  
Model Development ◽  
Mortality Rates ◽  
Average Deviation ◽  
Individual Tree ◽  
Permanent Sample Plots ◽  
Diameter Increment ◽  
Mortality Model

Abstract An individual-tree mortality model was developed for major tree species in complex stands (multi-cohort, multiaged, and mixed species) of southeastern British Columbia (BC), Canada. Data for 29,773 trees were obtained from permanent sample plots established in BC. Average annual diameter increment and mortality rates ranged from 0.08 to 0.17 cm/year and from 0.3 to 2.6%, respectively. Approximately 70% of the trees were used for model development and 30% for model evaluation. After evaluating the model, all 29,773 trees were used to fit the final model. A generalized logistic model was used to relate mortality to tree size, competition, and relative position of trees in a stand. The evaluation test demonstrated that the model appears to be well behaved and robust for the tree species considered in this study. For the eight tree species, the average deviation between observed and predicted annual mortality rates varied from −0.5 to 0.7% in the test data. West. J. Appl. For. 20(2):101–109.

scholarly journals Identifiability in age/period/cohort mortality models

2020 ◽  
Vol 14 (2) ◽  
pp. 500-536 ◽  
Author(s):  
Andrew Hunt ◽  
David Blake
Keyword(s):  
Mortality Rates ◽  
Comprehensive Analysis ◽  
Mortality Model ◽  
Mortality Models ◽  
The Future

AbstractThe addition of a set of cohort parameters to a mortality model can generate complex identifiability issues due to the collinearity between the dimensions of age, period and cohort. These issues can lead to robustness problems and difficulties making projections of future mortality rates. Since many modern mortality models incorporate cohort parameters, we believe that a comprehensive analysis of the identifiability issues in age/period/cohort mortality models is needed. In this paper, we discuss the origin of identifiability issues in general models before applying these insights to simple but commonly used mortality models. We then discuss how to project mortality models so that our forecasts of the future are independent of any arbitrary choices we make when fitting a model to data in order to identify the historical parameters.

Does it pay to delay social security?

2013 ◽  
Vol 13 (2) ◽  
pp. 121-144 ◽  
Author(s):  
JOHN B. SHOVEN ◽  
SITA NATARAJ SLAVOV
Keyword(s):  
Social Security ◽  
Interest Rates ◽  
Real Interest Rate ◽  
Mortality Rates ◽  
Present Value ◽  
Actuarial Fairness ◽  
Low Interest Rates ◽  
Social Security Benefits ◽  
To Receive ◽  
Mortality Improvements

AbstractSocial Security benefits may be commenced at any time between ages 62 and 70. As individuals who claim later can, on average, expect to receive benefits for a shorter period, an actuarial adjustment is made to the monthly benefit to reflect the age at which benefits are claimed. We investigate the actuarial fairness of that adjustment in light of recent improvements in mortality and historically low interest rates. We show that delaying is actuarially advantageous for a large number of people, even for individuals with mortality rates that are twice the average. At real interest rates closer to their historical average, singles with mortality that is substantially greater than average do not benefit from delay, although primary earners with high mortality can still improve the present value of the household's benefits through delay. We also investigate the extent to which the actuarial advantage of delay has grown since the early 1960s, when the choice of when to claim first became available, and we decompose this growth into three effects: (1) the effect of changes in Social Security's rules, (2) the effect of changes in the real interest rate, and (3) the effect of changes in life expectancy. Finally, we quantify the extent to which the gains from delay can be expected to increase in the future as a result of mortality improvements.

Theoretical Identifications of the Market Price of Risk under the Affine Interest Rate Model with Jumps

2005 ◽  
Vol 13 (2) ◽  
pp. 133-143
Author(s):  
Joon Hee Rhee
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Empirical Studies ◽  
Market Price ◽  
Rate Theory ◽  
Rate Model ◽  
Change Of Measure ◽  
Market Price Of Risk ◽  
Price Of Risk ◽  
Interest Rate Model

Any finance models must specify the market prices of risk that determines the relationship between the two probability measures. Although the general form of the change of measure is well known, few papers have investigated the change of measure for interest rate models and their implications for the way a model can fit to empirical facts about the behaviour of interest rates. This paper demonstrates that arbitrary specifications of market price of risk in empirical studies under the two factor affine interest rate model with jumps are not compatible with the theory of original interest rate model. Particularly, the empirical models of Duffee (2002) and Duarte (2003) may be wrong specifications in some parts under a rigorous theoretical interest rate theory.

Signaling and Indeterminacy of Equilibria in Unsecured Credit and Insurance Markets

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Shreemoy Mishra
Keyword(s):  
Interest Rates ◽  
Lower Risk ◽  
Market Failure ◽  
Strategic Behavior ◽  
Multiple Equilibria ◽  
Consumer Credit ◽  
Credit Market ◽  
Insurance Markets ◽  
Equilibrium Amount ◽  
Credit Scores

Abstract I study strategic behavior under ‘credit-based insurance.' It is assumed that higher consumer credit scores are associated with lower risk for insurable losses. Even when default is costless, some borrowers repay loans as a signal of low risk-type to insurers. There are multiple equilibria and equilibrium refinement techniques have no bite. The equilibrium amount of debt is indeterminate. For low credit scores, equilibrium involves randomization between default and repayment. This can explain the ‘hockey-stick' shape of interest rates observed in several markets. Perfect information about consumer risk-type can lead to credit-market failure and lower welfare.

scholarly journals Asymptotic behavior of critical, irreducible multi-type continuous state and continuous time branching processes with immigration

2016 ◽  
Vol 16 (04) ◽  
pp. 1650008 ◽  
Author(s):  
Mátyás Barczy ◽  
Gyula Pap
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Branching Processes ◽  
Bessel Process ◽  
Step Functions ◽  
Squared Bessel Process ◽  
Continuous State ◽  
Random Step ◽  
Branching Process With Immigration ◽  
Continuous Time Branching Processes

Under natural assumptions, a Feller type diffusion approximation is derived for critical, irreducible multi-type continuous state and continuous time branching processes with immigration. Namely, it is proved that a sequence of appropriately scaled random step functions formed from a critical, irreducible multi-type continuous state and continuous time branching process with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of a matrix related to the branching mechanism of the branching process in question.

Variable annuities and aggregate mortality risk

2016 ◽  
Vol 237 ◽  
pp. R55-R61 ◽  
Author(s):  
Martin Weale ◽  
Justin van de Ven
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Mortality Risk ◽  
Mortality Rates ◽  
Risk Averse ◽  
Actual Cost ◽  
Relative Risk Aversion ◽  
Variable Annuities ◽  
Actual Mortality ◽  
Specific Mortality

This paper explores the extent to which annuitants might be prepared to pay for protection against cohort-specific mortality risk, by comparing traditional indexed annuities with annuities whose payout rates are revised in response to differences between expected and actual mortality rates of the cohort in question. It finds that a man aged 65 with a coefficient of relative risk aversion of two would be prepared to pay 75p per £100 annuitised for protection against aggregate mortality risk while a man with risk aversion of twenty would be prepared to pay £5.75 per £100; studies put the actual cost at £2.70–£7 per £100, suggesting that unless annuitants are very risk averse it is likely that existing products tend to over-insure against cohort mortality risk.

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