Convex Duality in Constrained Portfolio Optimization

Cvitanić, Jakša; Karatzas, Ioannis

doi:10.1214/aoap/1177005576

Cited by 557 publications

(519 citation statements)

References 18 publications

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“…It has since been considered by numerous authors in a wide variety of settings. Contributions relevant to the setting considered in this paper include Cvitanic and Karatzas [17], who prove existence and uniqueness of the solution (optimal portfolio) to the utility maximization problem in a Brownian filtration when restricting investment strategies to convex sets; and Kallsen [46], who solves the continuous-time utility maximization problem in a market where asset prices follow exponential Lévy processes, both using the duality or martingale approach. For further references, see the review of Schachermayer [69].…”

Section: Introductionmentioning

confidence: 99%

Robust Portfolio Choice and Indifference Valuation

Laeven

Stadje²

2014

Mathematics of OR

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We solve, theoretically and numerically, the problems of optimal portfolio choice and indifference valuation in a general continuous-time setting. The setting features (i) ambiguity and ambiguity averse preferences, (ii) discontinuities in the asset price processes, with a general and possibly infinite activity jump part next to a continuous diffusion part, and (iii) general and possibly non-convex trading constraints. We characterize our solutions as solutions to Backward Stochastic Differential Equations (BSDEs). We prove existence and uniqueness of the solution to the general class of BSDEs with jumps having a drift (or driver) that grows at most quadratically, encompassing the solutions to our portfolio choice and valuation problems as special cases. We provide an explicit decomposition of the excess return on an asset into a risk premium and an ambiguity premium, and a further decomposition into a piece stemming from the diffusion part and a piece stemming from the jump part. We further compute our solutions in a few examples by numerically solving the corresponding BSDEs using regression techniques.

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Section: Introductionmentioning

confidence: 99%

Robust Portfolio Choice and Indifference Valuation

Laeven

Stadje²

2014

Mathematics of OR

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“…Cvitanic and Karatzas (1992) and other researchers (e.g. Schroder and Skiadis 2003) have shown that in many circumstances there is no duality gap.…”

Section: Dual Methods For Portfolio Optimizationmentioning

confidence: 90%

“…Since all of these methods are computationally intensive, it is expected that more sophisticated simulation techniques will have a greater role to play in future research. Moreover, in the context of portfolio optimization, there are many different 'formulations' of the duality theory (see Rogers 2003), and it is expected that many of these formulations can be used in a computational framework just as the dual formulation of Cvitanic and Karatzas (1992) was used in HKW (2003). This is a topic of ongoing research and simulation techniques will certainly be an important tool in furthering this agenda.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, HKW show how the duality theory of Cvitanic and Karatzas (1992) and others may be used to evaluate approximate solutions to difficult portfolio optimization problems. Their methods, which apply to problems in a multidimensional diffusion setting, should be of value when exact solutions are not available.…”

Section: Dual Methods For Portfolio Optimizationmentioning

confidence: 99%

“…In section 3.1 we describe the particular portfolio duality theory that was used in HKW and that was developed by Xu (1990), Xu (1992a, 1992b), Karatzas, Lehocky, Shreve and Xu (1991), and Cvitanic and Karatzas (1992).…”

Section: Portfolio Optimizationmentioning

confidence: 99%

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Duality theory and simulation in financial engineering

Haugh

Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693)

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This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is high-dimensional. In general, it is not possible to solve these problems exactly due to the so-called "curse of dimensionality" and as a result, approximate solution techniques are required. Approximate dynamic programming (ADP) and dual based methods have recently been proposed for constructing and evaluating good approximate solutions to these problems. In this paper we describe these ADP and dual-based methods, and the role simulation plays in each of them. Some directions for future research are also outlined.

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Continuous‐Time Asset Allocation

Zhou

2008

Encyclopedia of Quantitative Risk Analysis and Assessment

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Convex Duality in Constrained Portfolio Optimization

Cited by 557 publications

References 18 publications

Robust Portfolio Choice and Indifference Valuation

Robust Portfolio Choice and Indifference Valuation

Duality theory and simulation in financial engineering

Continuous‐Time Asset Allocation

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