Variable annuities: Market incompleteness and policyholder behavior

Moenig, Thorsten

doi:10.1016/j.insmatheco.2021.03.007

Cited by 7 publications

(3 citation statements)

References 45 publications

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“…Therefore, we construct the pooled model by modifying (3), (4), and (5). Assuming that the estimate of trend parameters are equal for both males and females, our expressions for the value of α, β, and ϛ in the pooled model are expressed as ( 9), (10), and (11) with adding a sex indicator denoted by s, with the value of 1 for males and 0 for females.…”

Section: Methodsmentioning

confidence: 99%

Forecasting Mortality Trend of Indonesian Old Aged Population with Bayesian Method

Chandra¹,

Abdullah²

2022

International Journal on Advanced Science, Engineering and Information Technology

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From around the nineteenth until the beginning of the twenty-first century, mortality rates show a declining trend. However, recent data on the United States population shows that the rate of decline started to slow down in the 2010s. Insurance companies need to be prepared in both ways: either mortality rates continue to decline, or there will be a turning point, and mortality rates start to increase. In this paper, we aim to get the whole picture of the mortality trend of Indonesian males, detect the possibility of a turning point in the mortality rates, and forecast mortality rates in the future. To reach this aim, we propose adjustments to the Makeham mortality model by including period and cohort information of the population via quadratic function. We also propose using the Bayesian method to estimate the parameters for the Indonesian old-aged males' population, where some adjustments were made in determining the priors, and the estimates were sampled from the posterior distribution using the Gibbs sampling algorithm. We found that our forecasting accuracy is satisfactory by considering the mean absolute percentage error values and coefficient of determination (R 2 ). We found that mortality rates are declining in the long term, but the probability of a turning point in the future is statistically significant. We identified two risks, longevity risk because of more centenarians in the future and mortality risk before their children complete compulsory education.

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Section: Methodsmentioning

confidence: 99%

Forecasting Mortality Trend of Indonesian Old Aged Population with Bayesian Method

Chandra¹,

Abdullah²

2022

International Journal on Advanced Science, Engineering and Information Technology

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“…For a broader perspective on the valuation of guaranteed benefit variable annuities, readers can refer to Feng and Jing (2017) [30], Feng and Yi (2019) [31], Liu (2021) [32], Moenig (2021) [33], and Gweon and Li (2023) [34] for additional insights and research outcomes.…”

Section: Related Literaturementioning

confidence: 99%

Valuation of a Mixture of GMIB and GMDB Variable Annuity

Han,

Li,

Fan

et al. 2024

Mathematics

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The Guaranteed Minimum Income Benefit (GMIB) and Guaranteed Minimum Death Benefit (GMDB) are options that may be included at the inception of a variable annuity (VA) contract. In exchange for small fees charged by the insurer, they give the policyholder a right to receive a guaranteed minimum level of annuity payment (GMIB) and a guaranteed minimum level of payment when the policyholder dies (GMDB), respectively. A combination of these two options may be attractive since it protects the policyholder’s investment from potential poor market behavior as well as mortality risk during the accumulation phase. This study examined the pricing of a composite variable annuity incorporating both the GMIB and GMDB options (a Guaranteed Minimum Income–Death Benefit, notated GMIDB). We used a non-arbitrage valuation method, decomposed the GMIDB value into two parts, and derived an analytical pricing formula based on a constant fee structure. The formula can be used to determine the fair fee to be charged. We conducted comprehensive sensitivity analyses on critical parameters to determine what drives the value of a GMIDB option. Our approach offers a simple and deterministic way to price a VA embedded with the GMIDB option. Our numerical findings suggested that the annuity conversion rate, age of the policyholder, and volatility of risky investments are significant in the valuation of a GMIDB option.

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“…Moenig (2021a) investigated the valuation and hedging problem of a portfolio of variable annuities via a dynamic programming method. Moenig (2021b) explored the impact of market incompleteness on the policyholder's behaviour. Wang & Zou (2021) solved the optimal fee structure for the GMDB and GMMB riders.…”

Section: Introductionmentioning

confidence: 99%

Pseudo-model-free hedging for variable annuities via deep reinforcement learning

Chong

Cui

2023

Ann. actuar. sci.

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This paper proposes a two-phase deep reinforcement learning approach, for hedging variable annuity contracts with both GMMB and GMDB riders, which can address model miscalibration in Black-Scholes financial and constant force of mortality actuarial market environments. In the training phase, an infant reinforcement learning agent interacts with a pre-designed training environment, collects sequential anchor-hedging reward signals, and gradually learns how to hedge the contracts. As expected, after a sufficient number of training steps, the trained reinforcement learning agent hedges, in the training environment, equally well as the correct Delta while outperforms misspecified Deltas. In the online learning phase, the trained reinforcement learning agent interacts with the market environment in real time, collects single terminal reward signals, and self-revises its hedging strategy. The hedging performance of the further trained reinforcement learning agent is demonstrated via an illustrative example on a rolling basis to reveal the self-revision capability on the hedging strategy by online learning.

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Variable annuities: Market incompleteness and policyholder behavior

Cited by 7 publications

References 45 publications

Forecasting Mortality Trend of Indonesian Old Aged Population with Bayesian Method

Forecasting Mortality Trend of Indonesian Old Aged Population with Bayesian Method

Valuation of a Mixture of GMIB and GMDB Variable Annuity

Pseudo-model-free hedging for variable annuities via deep reinforcement learning

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