Related papers: Concerning life annuities
The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic…
Euler gives a long introduction, giving all the arguments for and against the use of divergent series in calculus and then gives his own definition of the sum of a diverging series. Then in the second half of this paper he evaluates the the…
The number of people who receive a stable income for life from a closed pooled annuity fund is studied. Income stability is defined as keeping the income within a specified tolerance of the initial income in a fixed proportion of future…
Aggregated health data such as claims data from health insurances become more and more available for research purposes. Estimates of excess mortality from prevalence and incidence of a chronic condition have only been possible for ages 50…
Within the context of traditional life insurance, a model-independent relationship about how the market value of assets is attributed to the best estimate, the value of in-force business and tax is established. This relationship holds true…
Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.
Euler evaluates the integrals in the title and recognizes a recursion between them, which he then uses to give continued fractions for the log and arctan. The paper is translated from Euler's Latin original into German.
Translated from the Latin original, "De numeris amicabilibus" (1747). E100 in the Enestroem index. Euler starts by saying that with the success of mathematical analysis, number theory has been neglected. He argues that number theory is…
We investigate insurance purchases when bequest motives are age-varying and life insurance and life annuities both carry loads. The existing life cycle literature assumes bequests are normal goods without being either necessities or…
The main purpose of this work is to derive a partial differential equation for the reserves of life insurance liabilities subject to stochastic interest rates where the benefits and premiums depend directly on changes in the interest rate…
Translation from the Latin original, "Inventio summae cuiusque seriei ex dato termino generali" (1735). E47 in the Enestrom index. In this paper Euler derives the Euler-Maclaurin summation formula, by expressing y(x-1) with the Taylor…
This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap. Although swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, also provide…
In this article, we present several formulas that make it easier to compute the net single premiums when the mortality force over the fractional ages is assumed to be constant (C). More precisely, we compute the moments of the random…
How much do financial management fees cost investors? This article studies an approximate formula for the cumulative costs of annual Assets Under Management (AUM) fees. The formula states that an investment paying an annual fee of…
We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…
In this paper we provide a theoretical analysis of Variable Annuities with a focus on the holder's right to an early termination of the contract. We obtain a rigorous pricing formula and the optimal exercise boundary for the surrender…
Retirement prediction helps individuals and institutions make informed financial, lifestyle, and workforce decisions based on estimated retirement portfolios. This paper attempts to predict retirement using Monte Carlo simulations, allowing…
\noindent The modal age at death is an increasingly used measure for understanding longevity and mortality patterns. However, existing estimation methods focus on point estimates, overlooking the inherent variability and uncertainty in…
It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies, if the mortality force is a generic function of time and if the `subjective' life…
Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill…