Optimal lifetime consumption and investment under a drawdown constraint

Élie, Romuald; Touzi, Nizar

doi:10.1007/s00780-008-0066-8

Cited by 89 publications

(68 citation statements)

References 20 publications

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“…Grossman and Zhou (1993) and Cvitanic and Karatzas (1995) study the portfolio choice problem of an investor who maximizes power utility at a long horizon, subject to a constraint on the maximum drawdown (see also the recent paper of Elie and Touzi (2008) for an infinite horizon model with consumption, and the related work of Janecek and Sırbu (2010)). In other words, their investor solves the usual Merton problem, with the constraint that wealth cannot drop below a given fraction of the last recorded maximum.…”

Section: Drawdown Constraintsmentioning

confidence: 99%

The Incentives of Hedge Fund Fees and High-Water Marks

Guasoni

Obłój

2011

SSRN Journal

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Hedge fund managers receive performance fees proportional to their funds' profits, plus regular fees proportional to assets. Managers with constant relative risk aversion, constant investment opportunities, maximizing utility of fees at long horizons, choose constant Merton portfolios. The effective risk aversion depends on performance fees, which shrink the true risk aversion towards one. Thus, performance fees have ambiguous risk-shifting implications, depending on managers' own risk aversion. Further, managers behave like investors acting on their own behalf, but facing drawdown constraints. A Stackelberg equilibrium between investors and managers trades off the costs of performance fees, with their potential to align preferences. Only aggressive investors voluntarily pay high performance fees, and only if managers are even more aggressive.

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Section: Drawdown Constraintsmentioning

confidence: 99%

The Incentives of Hedge Fund Fees and High-Water Marks

Guasoni

Obłój

2011

SSRN Journal

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“…However, unlike the papers [15] and [6], our problem does not have a closed form solution. Therefore we need to prove that the Hamilton-Jacobi-Bellman equation has a smooth solution.…”

Section: Introductionmentioning

confidence: 94%

“…Since our model consists in controlling a reflected diffusion, where the reflection is actually coming from a running maximum, our problem is technically related to the problem of optimal investment with draw-down constrains in [8], [4], [15] and [6]. However, unlike the papers [15] and [6], our problem does not have a closed form solution.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment with High-watermark Performance Fee

Janeček¹,

Ŝırbu²

2012

SIAM J. Control Optim.

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We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge-fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic control problem is solved using dynamic programming arguments. We show by analytical methods that the associated Hamilton-Jacobi-Bellman equation has a smooth solution, and then obtain the existence and representation of the optimal control in feedback form using verification arguments.

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“…This technique has been already used in the case of HJB equations coming from optimal portfolio allocation problems (for which the nonlinearity in the second order term takes the form v 2 x /v xx ). We refer, e.g., to [Elie & Touzi, 2008] and [Schwartz & Tebaldi, 2006] in a lifetime consumption and investment problem, to [Gao, 2008] and [Xiao , Zhai & Qin, 2007] in the accumulation phase of a pension fund, to [Milevsky, Moore & Young, 2006], [Milevsky & Young, 2007] and [Gerrard, Højgaard & Vigna, 2012] in the decumulation phase of a pension fund. As mentioned in Section 2, the passage to the dual problem is made necessary by the coexistence of S and F in the same model, together with the quadratic loss function.…”

Section: Passage To a Dual Equationmentioning

confidence: 99%

“…Therefore, we use a known procedure from portfolio optimization, which allows us to transform the original equation into a nicer looking dual one. This procedure has been used, e.g., in [Elie & Touzi, 2008], [Gao, 2008], [Gerrard, Højgaard & Vigna, 2012], [Milevsky, Moore & Young, 2006], [Milevsky & Young, 2007] and [Xiao , Zhai & Qin, 2007]. In all such papers the dual equation is always linear.…”

Section: Introductionmentioning

confidence: 99%

Income drawdown option with minimum guarantee

Giacinto

Federico

Gozzi

et al. 2014

European Journal of Operational Research

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This paper deals with a constrained investment problem for a defined contribution (DC) pension fund where retirees are allowed to defer the purchase of the annuity at some future time after retirement.This problem has already been treated in the unconstrained case in a number of papers. The aim of this work is to deal with the more realistic case when constraints on the investment strategies and on the state variable are present. Due to the difficulty of the task, we consider, as a first step, the basic model of [Gerrard, Haberman & Vigna, 2004], where interim consumption and annuitization time are fixed. We extend their model by adding a no short-selling constraint on the control variable and a final capital requirement constraint on the state variable. This implies, in particular, no ruin.The mathematical problem is naturally formulated as a stochastic control problem with constraints on the control and the state variable, and is approached by the dynamic programming method. We write the non-linear Hamilton-Jacobi-Bellman equation for the problem and transform it into a dual one that is semi-linear, following a well-established duality procedure. In the special relevant case without running cost, we explicitly compute the value function for the problem and give the optimal strategy in feedback form. A numerical application ends the paper and shows the extent of applicability of the model to a DC pension fund in the decumulation phase.J.E.L. classification: C61, G11, G23. A.M.S. classification: 91B28, 93E20, 49L25.Keywords: pension fund, decumulation phase, constrained portfolio, stochastic optimal control, dynamic programming, Hamilton-Jacobi-Bellman equation. Acknowledgements:We thank three anonymous reviewers for thorough reading and the editor for careful handling of the paper.

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Optimal lifetime consumption and investment under a drawdown constraint

Cited by 89 publications

References 20 publications

The Incentives of Hedge Fund Fees and High-Water Marks

The Incentives of Hedge Fund Fees and High-Water Marks

Optimal Investment with High-watermark Performance Fee

Income drawdown option with minimum guarantee

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