Portfolio Management With Constraints

Boyle, Phelim; Tian, Weidong

doi:10.1111/j.1467-9965.2007.00306.x

Cited by 61 publications

(43 citation statements)

References 41 publications

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“…This was already used in Bernard, Boyle and Vanduffel [1], Bernard and Vanduffel [5] and in Bernard, Chen and Vandufel [2]. Let us give an example of application of Theorem 4 which extends the probability constraint considered in Boyle and Tian [6].…”

Section: Bounds On Capital Requirementsmentioning

confidence: 97%

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Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence

Bernard¹,

Liu

MacGillivray

et al. 2013

Dependence Modeling

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Nelsen et al. [20] find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov [25] generalizes this work by giving explicit expressions for the best upper and lower bounds for a bivariate copula when its values on a compact subset of [0 1] 2 are known. He shows that they are quasi-copulas and not necessarily copulas. Tankov [25] and Bernard et al. [3] both give sufficient conditions for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that both bounds are simultaneously copulas. Furthermore, we develop a novel application to quantitative risk management by computing bounds on a bivariate risk measure. This can be useful in optimal portfolio selection, in reinsurance, in pricing bivariate derivatives or in determining capital requirements when only partial information on dependence is available. Nelsen [18] derives best possible bounds when the copula is known at a specific point. Our objective in this paper is to extend this literature to the case when the copula is known in more than one point and to show how these bounds can be useful in quantifying dependence misspecification. Assuming that marginals are given and that the dependence is unspecified, or partly unspecified, bounds on copulas can be indeed used to quantify this type of model risk. ). Tankov shows that they are quasi-copulas and not necessarily copulas. In this paper, we focus on deriving bounds on copulas that are also copulas. The first section focuses on finding simple conditions to ensure that Tankov's bounds are copulas. When the bounds are not copulas, it is possible to approximate them by a copula. The second section illustrates a method to find the best copula for the uniform norm that approximates the * Keywords

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Section: Bounds On Capital Requirementsmentioning

confidence: 97%

“…In Example 3 of Bernard, Boyle and Vanduffel [1], they consider a Black Scholes market and assume that an investor wants to achieve the same distribution F as an investment in the risky asset S T but is subject to additional constraints 6 .…”

Section: Examplementioning

confidence: 99%

Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence

Bernard¹,

Liu

MacGillivray

et al. 2013

Dependence Modeling

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“…Example 2 Value-at-Risk with random level L: Such a constraint was considered by Boyle & Tian (2007) We then obtain for the shortfall probability…”

Section: The Optimization Problemmentioning

confidence: 99%

“…The type of optimization problem we consider in our paper belongs to the class of so-called non-convex optimization problems. Such problems, in the setting of optimal investment problems in complete markets, have been considered previously by Boyle & Tian (2007).…”

Section: Introductionmentioning

confidence: 99%

Utility Maximization Under Solvency Constraints and Unhedgeable Risks

Kleinow

Pelsser

2009

SSRN Journal

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We consider the utility maximization problem for an investor who faces a solvency or risk constraint in addition to a budget constraint. The investor wishes to maximize her expected utility from terminal wealth subject to a bound on her expected solvency at maturity. We measure solvency using a solvency function applied to the terminal wealth. The motivation for our analysis is an optimal investment problem where the investor faces a random and non-hedgable liability at maturity.

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“…As in BASAK and SHAPIRO [2001], these are imposed at time 0 and not reevaluated later. BOYLE and TIAN [2007], GABIH, GRECKSCH, RICHTER and WUNDERLICH [2006], and BASAK, SHAPIRO and TEPLA [2006] solve versions of problem (10.3) if investors compare their performance to a random benchmark at the time horizon T . GABIH, GRECKSCH, RICHTER and WUN-DERLICH [2006] focus on a Black-Scholes market with limits on the expected utility loss and derive explicit results.…”

Section: Semi-dynamic Risk Constraintsmentioning

confidence: 99%