5,947 research outputs found
A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing
In this article we investigate a state-space representation of the Lee-Carter
model which is a benchmark stochastic mortality model for forecasting
age-specific death rates. Existing relevant literature focuses mainly on
mortality forecasting or pricing of longevity derivatives, while the full
implications and methods of using the state-space representation of the
Lee-Carter model in pricing retirement income products is yet to be examined.
The main contribution of this article is twofold. First, we provide a rigorous
and detailed derivation of the posterior distributions of the parameters and
the latent process of the Lee-Carter model via Gibbs sampling. Our assumption
for priors is slightly more general than the current literature in this area.
Moreover, we suggest a new form of identification constraint not yet utilised
in the actuarial literature that proves to be a more convenient approach for
estimating the model under the state-space framework. Second, by exploiting the
posterior distribution of the latent process and parameters, we examine the
pricing range of annuities, taking into account the stochastic nature of the
dynamics of the mortality rates. In this way we aim to capture the impact of
longevity risk on the pricing of annuities. The outcome of our study
demonstrates that an annuity price can be more than 4% under-valued when
different assumptions are made on determining the survival curve constructed
from the distribution of the forecasted death rates. Given that a typical
annuity portfolio consists of a large number of policies with maturities which
span decades, we conclude that the impact of longevity risk on the accurate
pricing of annuities is a significant issue to be further researched. In
addition, we find that mis-pricing is increasingly more pronounced for older
ages as well as for annuity policies having a longer maturity.Comment: 9 pages; conference pape
A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting
This paper explores and develops alternative statistical representations and
estimation approaches for dynamic mortality models. The framework we adopt is
to reinterpret popular mortality models such as the Lee-Carter class of models
in a general state-space modelling methodology, which allows modelling,
estimation and forecasting of mortality under a unified framework. Furthermore,
we propose an alternative class of model identification constraints which is
more suited to statistical inference in filtering and parameter estimation
settings based on maximization of the marginalized likelihood or in Bayesian
inference. We then develop a novel class of Bayesian state-space models which
incorporate apriori beliefs about the mortality model characteristics as well
as for more flexible and appropriate assumptions relating to heteroscedasticity
that present in observed mortality data. We show that multiple period and
cohort effect can be cast under a state-space structure. To study long term
mortality dynamics, we introduce stochastic volatility to the period effect.
The estimation of the resulting stochastic volatility model of mortality is
performed using a recent class of Monte Carlo procedure specifically designed
for state and parameter estimation in Bayesian state-space models, known as the
class of particle Markov chain Monte Carlo methods. We illustrate the framework
we have developed using Danish male mortality data, and show that incorporating
heteroscedasticity and stochastic volatility markedly improves model fit
despite an increase of model complexity. Forecasting properties of the enhanced
models are examined with long term and short term calibration periods on the
reconstruction of life tables.Comment: 46 page
Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes
In this paper we prove exact forms of large deviations for local times and
intersection local times of fractional Brownian motions and Riemann-Liouville
processes. We also show that a fractional Brownian motion and the related
Riemann-Liouville process behave like constant multiples of each other with
regard to large deviations for their local and intersection local times. As a
consequence of our large deviation estimates, we derive laws of iterated
logarithm for the corresponding local times. The key points of our methods: (1)
logarithmic superadditivity of a normalized sequence of moments of
exponentially randomized local time of a fractional Brownian motion; (2)
logarithmic subadditivity of a normalized sequence of moments of exponentially
randomized intersection local time of Riemann-Liouville processes; (3)
comparison of local and intersection local times based on embedding of a part
of a fractional Brownian motion into the reproducing kernel Hilbert space of
the Riemann-Liouville process.Comment: To appear in the Annals of Probabilit
Bounds for Kloosterman sums on GL(n)
This paper establishes power-saving bounds for Kloosterman sums associated
with the long Weyl element for GL(n), as well as for another type of Weyl
element of order 2. These bounds are obtained by establishing an explicit
representation as exponential sums. As an application we go beyond Sarnak's
density conjecture for the principal congruence subgroup of prime level. We
also bound all Kloosterman sums for GL(4).Comment: 20 page
Evidence for sub-Chandrasekhar Type Ia supernovae from the last major merger
We investigate the contribution of sub-Chandrasekhar mass Type Ia supernovae to the chemical enrichment of the Gaia Sausage galaxy, the progenitor of a significant merger event in the early life of the Milky Way. Using a combination of data from Nissen & Schuster (2010), the 3rd GALAH data release (with 1D NLTE abundance corrections) and APOGEE data release 16, we fit analytic chemical evolution models to a 9-dimensional chemical abundance space (Fe, Mg, Si, Ca, Cr, Mn, Ni, Cu, Zn) in particular focusing on the iron-peak elements, Mn and Ni. We find that low [Mn/Fe] and low [Ni/Fe] Type Ia yields are required to explain the observed trends beyond the [/Fe] knee of the Gaia Sausage (approximately at [Fe/H] ). Comparison to theoretical yield calculations indicate a significant contribution from sub-Chandrasekhar mass Type Ia supernovae in this system (from % to % depending on the theoretical model with an additional % systematic from NLTE corrections). We compare to results from other Local Group environments including dwarf spheroidal galaxies, the Magellanic Clouds and the Milky Way's bulge, finding the Type Ia [Mn/Fe] yield must be metallicity-dependent. Our results suggest that sub-Chandrasekhar mass channels are a significant, perhaps even dominant, contribution to Type Ia supernovae in metal-poor systems, whilst more metal-rich systems could be explained by metallicity-dependent sub-Chandrasekhar mass yields, possibly with additional progenitor mass variation related to star formation history, or an increased contribution from Chandrasekhar mass channels at higher metallicity
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