The annuity puzzle revisited: a deterministic version with Lagrangian methods
(2006) Belgian Actuarial Bulletin — Vol. 6, n° 1, p. 40-48 (2006)
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- Authors
- Abstract
- This paper revisits the issue of the annuity puzzle. We determine the optimal consumption strategy of an individual, without any bequest motive, who allocates his wealth between life annuities and cash. The budget constraint, which specifies that the individual doesn’t borrow to consume, is inserted in the Hamilton Jacobi Bellman equation with a Lagrange multiplier. The optimal planning of consumption is divided into two periods and the transition time is calculated numerically. Finally, we show the influence of cash return and of age on the optimal allocation of initial wealth between a life annuity and cash.
- Affiliations
Louvain School of Management CESAM - Center for Studies in Asset Management
Citations
Devolder, P., & Hainaut, D. (2006). The annuity puzzle revisited: a deterministic version with Lagrangian methods. Belgian Actuarial Bulletin, 6(1), 40-48. https://hdl.handle.net/2078.5/34621 (Original work published 2006)