Affine Processes for Dynamic Mortality and Actuarial Valuations

Biffis, Enrico

doi:10.2139/ssrn.647421

Cited by 92 publications

(140 citation statements)

References 47 publications

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“…investment accounts) and scale withdrawals by the value of the assets, they decline by approximately 4% per year. That number would represent the population average spending rate 3 and is uncannily close to the widely used (among financial planners) 4% rule, proposed by William Bengen in the early 1990s. 3 Strictly speaking we should adjust our figures to account for asset returns.…”

Section: Introductionsupporting

confidence: 54%

Retirement Spending and Biological Age

2017

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We solve a lifecycle model in which the consumer's chronological age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in time like a broken clock that might occasionally move backwards. In other words, biological age could actually decline. Our paper is inspired by the growing body of medical literature that has identified biomarkers which indicate how people age at different rates. This offers better estimates of expected remaining lifetime and future mortality rates. It isn't farfetched to argue that in the not-too-distant future personal age will be more closely associated with biological vs. calendar age. Thus, after introducing our stochastic mortality model we derive optimal consumption rates in a classic Yaari (1965) framework adjusted to our proper clock time. In addition to the normative implications of having access to biological age, our positive objective is to partially explain the cross-sectional heterogeneity in retirement spending rates at any given chronological age. In sum, we argue that neither biological nor chronological age alone is a sufficient statistic for making economic decisions. Rather, both ages are required to behave rationally.

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Section: Introductionsupporting

confidence: 54%

Retirement Spending and Biological Age

2017

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“…In this setting, we study unit-linked life insurance liabilities in the form of insurance payment streams as introduced by Møller (2001). It is now widely acknowledged (see, e.g., Møller 1998;Biffis 2005;Barbarin 2008) that most payment streams of practical relevance are covered by the three building blocks consisting of term insurance, annuity, and pure endowment contracts. Following Barbarin (2008) and Møller (1998), the term insurance contract is defined by the following portfolio payoff structure:…”

Section: The Combined Modelmentioning

confidence: 99%

Risk‐minimization for Life Insurance Liabilities With Dependent Mortality Risk

Biagini

Botero

Schreiber

2015

Mathematical Finance

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In this paper, we study the pricing and hedging of typical life insurance liabilities for an insurance portfolio with dependent mortality risk by means of the well-known risk-minimization approach. As the insurance portfolio consists of individuals of different age cohorts in order to capture the cross-generational dependency structure of the portfolio, we introduce affine models for the mortality intensities based on Gaussian random fields that deliver analytically tractable results. We also provide specific examples consistent with historical mortality data and correlation structures. Main novelties of this work are the explicit computations of risk-minimizing strategies for life insurance liabilities written on an insurance portfolio composed of primary financial assets (a risky asset and a money market account) and a family of longevity bonds, and the simultaneous consideration of different age cohorts.

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“…As an example we consider a generalized Cox-Ingersoll-Ross model to represent the trend of the mortality intensity µ, see , e.g. Dahl [20], Biffis [7]. In Biffis [7], mortality intensity of the sample population follows an affine dynamics with stochastic drift, given by…”

Section: Modeling Frameworkmentioning

confidence: 99%