The Capital Growth Theory of Investment: Part I

Ziemba, Bill

doi:10.1002/wilm.42820020110

Cited by 7 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See also the papers Ziemba (2003Ziemba ( , 2004 for some easy-toread accounts. A standard reference in gambling is the book Thorp (1966).…”

Section: Notesmentioning

confidence: 99%

“…Some recent support is found in McEnally (1986), Aurell, Baviera, Hammarlid, Serva, and Vulpiani (2000), Michaud (2003) and Platen (2005b). The view that investment of more than 100% in the GOP is irrational is common in the gambling literature -referred to as "overbetting" and is found for instance in Ziemba (2003Ziemba ( , 2004Ziemba ( , 2005. In a finance context the argument is voiced in Platen (2005c).…”

Section: Notesmentioning

confidence: 99%

See 1 more Smart Citation

On the History of the Growth-Optimal Portfolio

Christensen

2012

Advances in Computer Science and Engineering: Texts

View full text Add to dashboard Cite

The growth optimal portfolio (GOP) is a portfolio which has a maximal expected growth rate over any time horizon. As a consequence, this portfolio is sure to outperform any other significantly different strategy as the time horizon increases. This property in particular has fascinated many researchers in finance and mathematics created a huge and exciting literature on growth optimal investment. This paper attempts to provide a comprehensive survey of the literature and applications of the GOP. In particular, the heated debate of whether the GOP has a special place among portfolios in the asset allocation decision is reviewed as this still seem to be an area where some misconceptions exists. The survey also provides an extensive review of the recent use of the GOP as a pricing tool, in for instance the so-called "benchmark approach". This approach builds on the numéraire property of the GOP, that is, the fact that any other asset denominated in units of the GOP become a supermartingale

show abstract

“…See also the papers Ziemba (2003Ziemba ( , 2004 for some easy-toread accounts. A standard reference in gambling is the book Thorp (1966).…”

Section: Notesmentioning

confidence: 99%

Section: Notesmentioning

confidence: 99%

On the History of the Growth-Optimal Portfolio

Christensen

2012

Advances in Computer Science and Engineering: Texts

View full text Add to dashboard Cite

show abstract

“…The long-term out-performance of any other strictly positive portfolio has been studied by Breiman [3], Markowitz [10], Algoet and Cover [2]. For an overview, see Hakansson and Ziemba [6], Ziemba [13] and Platen [11].…”

Section: Introductionmentioning

confidence: 99%

On the Consumption/Distribution Theorem Under the Long-Run Growth Criterion Subject to a Drawdown Constraint

Klass

Nowicki

2010

Int. J. Theor. Appl. Finan.

View full text Add to dashboard Cite

Consider any discrete time sequence of investment fortunes Fn which has a finite long-run growth rate V (r, λ * ) = limn→∞ ln Fn n when subject to the present value capital drawdown constraint Fne −rn ≥ λ * max 0≤k≤n F k e −rk , where 0 ≤ λ * < 1, in the presence of a riskless asset affording a return of e r 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. Int. J. Theor. Appl. Finan. 2010.13:931-957. Downloaded from www.worldscientific.com by INDIANA UNIVERSITY @ BLOOMINGTON on 03/16/15. For personal use only. Int. J. Theor. Appl. Finan. 2010.13:931-957. Downloaded from www.worldscientific.com by INDIANA UNIVERSITY @ BLOOMINGTON on 03/16/15. For personal use only.

show abstract

“…With simple strategies and constant, identical saving rates across investors, the sole survivor is the portfolio rule known as 'betting your beliefs' (Breiman, 1961), where the proportion of wealth placed on each asset is the probability of the corresponding state of nature. This strategy can also be generated by maximizing the expected logarithm of relative returns, which is known as the Kelly rule, studied in discrete time by Kelly (1956), Breiman (1961), Thorp (1971) and Hakansson and Ziemba (1995) (for an overview, see also Ziemba, 2002) and, in continuous-time, by Pestien and Sudderth (1985), Heath et al (1987) and Karatzas and Shreve (1998), among others. Hens and Schenk-Hoppe´(2005) proposed a more general setting, with incomplete markets, general short-lived assets that are reborn each time, and constant, positive, proportional, and identical saving rates across investors.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary portfolio selection with liquidity shocks

Giorgi

2008

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

The wealth dynamics of insurance companies strongly depends on the success of their investment strategies, but also on liquidity shocks which occur during unfavorable years, when indemnities to be paid to the clients exceed collected premia. An investment strategy that does not take liquidity shocks into account, exposes insurance companies to the risk of bankruptcy.This paper analyzes the behavior of insurance companies in an evolutionary framework. We show that an insurance company that merely satisfies regulatory constraints will eventually vanish from the market. We give a more restrictive no-bankruptcy condition on investment strategies. Moreover, we characterize trading strategies that are evolutionary stable, i.e., able to drive out any mutation. We study the existence of such strategies and the conditions under which financial and insurance markets are stable. r

show abstract

The Capital Growth Theory of Investment: Part I

Cited by 7 publications

References 0 publications

On the History of the Growth-Optimal Portfolio

On the History of the Growth-Optimal Portfolio

On the Consumption/Distribution Theorem Under the Long-Run Growth Criterion Subject to a Drawdown Constraint

Evolutionary portfolio selection with liquidity shocks

Contact Info

Product

Resources

About