An Investment Strategy with Overshoot Rebates which Minimizes the Time to Attain a Specified Goal

Aucamp, Donald C.

doi:10.1287/mnsc.23.11.1234

Cited by 11 publications

(9 citation statements)

References 5 publications

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“…Condition (2 ′ ) of Proposition 2.2 obviously implies Assumption 2.1 (2). Conversely, assume that Assumptions 2.1 are in force.…”

Section: Proofsmentioning

confidence: 99%

“…We shall frequently refer to the numéraire portfolio as the growth-optimal portfolio, as the two notions coincide. Assumption 2.1 (2) constitutes what has been coined a "favorable game" in [5] and it is necessary in order for the problem described in (2.3) to have finite value and therefore to be well-posed. Under Assumption 2.1 (2), and in view of the property X (x) = xX (1) for x ∈ R + , it is obvious that for all…”

Section: Standing Assumptionsmentioning

confidence: 99%

“…As we did in the case of exponential Lévy markets, we shall use statements (1), (2) and ( . As explained in §2.2, for given x < ℓ, our aim is to find the wealth process X ∈ X (x) that minimizes E [T (X; ℓ)].…”

Section: 2mentioning

confidence: 99%

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Minimizing the Expected Market Time to Reach a Certain Wealth Level

Kardaras¹,

Platen²

2010

SIAM J. Finan. Math.

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Abstract. In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Lévy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Itô market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor's point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.

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“…Condition (2 ′ ) of Proposition 2.2 obviously implies Assumption 2.1 (2). Conversely, assume that Assumptions 2.1 are in force.…”

Section: Proofsmentioning

confidence: 99%

Section: Standing Assumptionsmentioning

confidence: 99%

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Minimizing the Expected Market Time to Reach a Certain Wealth Level

Kardaras¹,

Platen²

2010

SIAM J. Finan. Math.

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“…The expected time to reach a certain goal was considered inBreiman (1961) and the inclusion of a rebate in Aucamp (1977) implies that the GOP will minimize this time for finite levels of wealth.…”

Section: Notesmentioning

confidence: 99%

On the History of the Growth-Optimal Portfolio

Christensen

2012

Advances in Computer Science and Engineering: Texts

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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

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“…This property is established at various levels of generality inBreiman (1961),Aucamp (1977),Heath and Sudderth (1984),Heath et al (1987),Browne (1999), andKardaras and Platen (2010).…”

mentioning

confidence: 97%

The Incentives of Hedge Fund Fees and High‐water Marks

Guasoni

Obłój

2013

Mathematical Finance

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Hedge fund managers receive a large fraction of their funds' profits, paid when funds exceed their high-water marks. We study the incentives of such performance fees. A manager with long-horizon, constant investment opportunities and relative risk aversion, chooses a constant Merton portfolio. However, the effective risk aversion shrinks toward one in proportion to performance fees. Risk shifting implications are ambiguous and depend on the manager's own risk aversion. Managers with equal investment opportunities but different performance fees and risk aversions may coexist in a competitive equilibrium. The resulting leverage increases with performance fees-a prediction that we confirm empirically.

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An Investment Strategy with Overshoot Rebates which Minimizes the Time to Attain a Specified Goal

Cited by 11 publications

References 5 publications

Minimizing the Expected Market Time to Reach a Certain Wealth Level

Minimizing the Expected Market Time to Reach a Certain Wealth Level

On the History of the Growth-Optimal Portfolio

The Incentives of Hedge Fund Fees and High‐water Marks

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