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On the consumption/distribution theorem under the long-run growth criterion subject to a drawdown constraint

Klass, Michael J. and Nowicki, Krzysztof LU (2010) In International Journal of Theoretical and Applied Finance 13(6). p.931-957
Abstract
Consider any discrete time sequence of investment fortunes Fn which has a finite long-run growth rate when subject to the present value capital drawdown constraint Fne-rn ≥ λ* max0≤k≤nFke-rk, where 0 ≤ λ* < 1, in the presence of a riskless asset affording a return of er dollars per time period per dollar invested. We show that money can be withdrawn for consumption from the invested capital without either reducing the long-run growth rate of such capital or violating the drawdown constraint for our capital sequence, while simultaneously increasing the amount of capital withdrawn for consumption at the identical long-term rate of V(r, λ*). We extend this result to an exponentially increasing number of consumption categories and discuss... (More)
Consider any discrete time sequence of investment fortunes Fn which has a finite long-run growth rate when subject to the present value capital drawdown constraint Fne-rn ≥ λ* max0≤k≤nFke-rk, where 0 ≤ λ* < 1, in the presence of a riskless asset affording a return of er dollars per time period per dollar invested. We show that money can be withdrawn for consumption from the invested capital without either reducing the long-run growth rate of such capital or violating the drawdown constraint for our capital sequence, while simultaneously increasing the amount of capital withdrawn for consumption at the identical long-term rate of V(r, λ*). We extend this result to an exponentially increasing number of consumption categories and discuss how additional yearly contributions can temporarily augment the total capital under management. In addition, we assess the short-term practicality of creating such an endowment/consumption/distribution program. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Long-run growth, infinite horizon investment and consumption categories, log utility, withdrawal strategy, distribution strategy, consumption/distribution theorem, draw-down constraint, intergenerational trusts
in
International Journal of Theoretical and Applied Finance
volume
13
issue
6
pages
931 - 957
publisher
World Scientific
external identifiers
  • scopus:77956329377
ISSN
0219-0249
DOI
10.1142/S0219024910006054
language
English
LU publication?
yes
id
a55ead90-d734-4c11-8127-27f022e46b80 (old id 1668813)
date added to LUP
2010-09-20 10:57:49
date last changed
2018-05-29 11:39:30
@article{a55ead90-d734-4c11-8127-27f022e46b80,
  abstract     = {Consider any discrete time sequence of investment fortunes Fn which has a finite long-run growth rate when subject to the present value capital drawdown constraint Fne-rn ≥ λ* max0≤k≤nFke-rk, where 0 ≤ λ* &lt; 1, in the presence of a riskless asset affording a return of er dollars per time period per dollar invested. We show that money can be withdrawn for consumption from the invested capital without either reducing the long-run growth rate of such capital or violating the drawdown constraint for our capital sequence, while simultaneously increasing the amount of capital withdrawn for consumption at the identical long-term rate of V(r, λ*). We extend this result to an exponentially increasing number of consumption categories and discuss how additional yearly contributions can temporarily augment the total capital under management. In addition, we assess the short-term practicality of creating such an endowment/consumption/distribution program.},
  author       = {Klass, Michael J. and Nowicki, Krzysztof},
  issn         = {0219-0249},
  keyword      = {Long-run growth,infinite horizon investment and consumption categories,log utility,withdrawal strategy,distribution strategy,consumption/distribution theorem,draw-down constraint,intergenerational trusts},
  language     = {eng},
  number       = {6},
  pages        = {931--957},
  publisher    = {World Scientific},
  series       = {International Journal of Theoretical and Applied Finance},
  title        = {On the consumption/distribution theorem under the long-run growth criterion subject to a drawdown constraint},
  url          = {http://dx.doi.org/10.1142/S0219024910006054},
  volume       = {13},
  year         = {2010},
}