Related papers: Concerning life annuities
In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas.
In this paper, we are concerned with the valuation of Guaranteed Annuity Options (GAOs) under the most generalised modelling framework where both interest and mortality rates are stochastic and correlated. Pricing these type of options in…
There is sustained and widespread interest in understanding the limit, if any, to the human lifespan. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
The state-of-the-art proposes Life Care Annuities, that have been recently designed as variable annuity contracts with Long-Term Care payouts and Guaranteed Lifelong Withdrawal Benefits. In this paper, we propose more general features for…
Catalan's formula, for the portion of the inheritance that a legitimate child of a 19th-century deceased French gentleman should receive, is given a new proof (using Difference Operators), and generalized. Another, more computationally…
There is growing interest in the design of pension annuities that insure against idiosyncratic longevity risk while pooling and sharing systematic risk. This is partially motivated by the desire to reduce capital and reserve requirements…
In this study we propose a unified model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature and provide a general methodology to solve the model.…
In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time…
This is a translation of Euler's Latin paper "De fractionibus continuis observationes" into English. In this paper Euler describes his theory of continued fractions. He teaches, how to transform series into continued fractions, solves the…
E30 in the Enestrom index. Translated from the Latin original "De formis radicum aequationum cuiusque ordinis coniectatio" (1733). For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are…
We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for…
This paper introduces a recurrent neural network approach for predicting user lifetime value in Software as a Service (SaaS) applications. The approach accounts for three connected time dimensions. These dimensions are the user cohort (the…
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the…
We prove the existence of a Radner equilibrium in a model with population growth and analyze the effects on asset prices. A finite population of agents grows indefinitely at a Poisson rate, while receiving unspanned income and choosing…
Financial forecasting is a difficult task due to the intrinsic complexity of the financial system. In the present paper we relate our experience using neural nets as financial time series forecast method. In particular we show that a neural…
We introduce a new pension product that offers retirees the opportunity for a lifelong income and a bequest for their estate. Based on a tontine mechanism, the product divides pension savings between a tontine account and a bequest account.…
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…
We revisited an analysis made by Euler in a memoir of 1753 'Sur une nouvelle maniere d'elever de l'eau propose par M. de Mour' (On a new method to raise water proposed by Mr. de Mour), addressing a type of water sprinkler, consisting of an…
Each individual in society experiences an evolution of their income during their lifetime. Macroscopically, this dynamics creates a statistical relationship between age and income for each society. In this study, we investigate income…