scholarly journals Life Annuitization: Why and how Much?

2006 ◽  
Vol 36 (2) ◽  
pp. 629-654 ◽  
Author(s):  
Donatien Hainaut ◽  
Pierre Devolder
Keyword(s):  
Asset Allocation ◽  
Risky Asset ◽  
Optimal Planning ◽  
Markov Chain Approximation ◽  
Investment Pattern ◽  
Life Annuity ◽  
Bequest Motive ◽  
Future Consumption ◽  
Life Annuities ◽  
Chain Approximation

This paper addresses some of the problems a majority of retired individuals face: Why and in what proportion should they invest in a life annuity to maximize the utility of their future consumption or a bequest? The market considered in this work is made up of three assets: a life annuity, a risky asset and a cash account. As this problem doesn’t accept any suitable explicit solution, it is numerically solved by the Markov Chain approximation developed by Kushner and Dupuis. Without a bequest motive, we observe that the optimal planning of consumption is divided into two periods and that optimal asset allocation should include the risky asset. Next, the influence of a bequest on consumption and investment pattern is developed. We demonstrate that even with a bequest motive, pensioners should allocate a part of their wealth to the purchase of life annuities.

Demand for life annuities from married couples with a bequest motive

2006 ◽  
Vol 5 (2) ◽  
pp. 197-229 ◽  
Author(s):  
CARLOS VIDAL-MELIÁ ◽  
ANA LEJÁRRAGA-GARCÍA
Keyword(s):  
Married Couples ◽  
Combined Effects ◽  
Defined Benefit ◽  
Defined Contribution ◽  
Relevant Feature ◽  
Policy Makers ◽  
Life Annuity ◽  
Bequest Motive ◽  
Annuity Markets ◽  
Life Annuities

The aim of this paper is to explain the ‘annuities puzzle’ in greater depth by introducing the bequest motive. It will try to determine whether this motive really is a relevant feature influencing the demand for life annuities from married couples. With this aim in mind, we develop an optimization model of the utility provided by purchasing a life annuity with contingent survivor benefit or a joint survivor life annuity. Our model is based on that first put forward by Brown and Poterba (2000), to which we have added elements from other models, such as Friedman and Warshawsky's (1990) and Vidal and Lejárraga's (2004), which include the bequest motive. This will enable us to calculate the annuity equivalent wealth and the optimal percentage of wealth to annuitize in various contexts: the possibility of access to actuarially fair annuity markets, the inclusion of so-called market imperfections, and the assumption that couples already have part of their wealth in pre-existing life annuities. Numerical results are presented for the case of Spain. The bequest motive is found not to be a significant factor influencing the demand for annuities from couples. Indeed very few couples would be willing to purchase them once we take into account the combined effects of market imperfections, the possibility of pre-existing annuities and the bequest motive. These findings have repercussions for policy makers regulating defined contribution capitalization systems, which are complementary to defined benefit systems.

scholarly journals Markov chain approximation of one-dimensional sticky diffusions

2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang
Keyword(s):  
Markov Chain ◽  
Approximate Solutions ◽  
Price Model ◽  
One Dimensional ◽  
Markov Chain Approximation ◽  
Alternative Approaches ◽  
Second Order Convergence ◽  
Chain Approximation ◽  
Matrix Exponentials ◽  
Interior Points

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.

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