Inverse portfolio problem with mean-deviation model

Grechuk, Bogdan; Zabarankin, Michael

doi:10.1016/j.ejor.2013.04.056

Cited by 29 publications

(28 citation statements)

References 15 publications

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“…, n. Thus, Q * is a risk-neutral r.v. If ρ(X) ≡ −E[X], then Q * is comonotone with −X * by Proposition 14 in [12], applied to the functional D(X) = ρ(X) + E[X]. If ρ(X) ≡ −E[X] then Q * ≡ 1, and comonotonicity follows as well.…”

Section: Propositionmentioning

confidence: 87%

“…For example, the standard deviation is not lower range dominated, and as a result, it has no counterpart in coherent risk measures through the one-to-one correspondence established in [27,28]. Also, the work [12] assumes X * to be SSD-efficient to guarantee the existence of a law invariant solution, which is no longer required here.…”

Section: Introductionmentioning

confidence: 93%

“…with Q M defined by either (10), (11), or (12), if the agent requires ρ to conform to preference conditions (a), (b), or (c), respectively.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…This approach was demonstrated in identifying a deviation measure in a Markowitz-type portfolio selection problem; see [12] and [36,Section 8.2.4]. However, in general, the results in [12] cannot be used directly to solve the inverse portfolio problem with an unrestricted class of coherent risk measures, since deviation measures correspond one-to-one to averse measures of risk [27,28], 1 which, in contrast to coherent risk measures, are not required to preserve monotonicity of preference relations; see [27,28] and [36,Section 2.3]. In fact, these two classes of risk measures have a nonempty intersection called coherent averse measures of risk that correspond one-to-one to lower range dominated deviation measures (subclass of general deviation measures).…”

Section: Introductionmentioning

confidence: 99%

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Inverse portfolio problem with coherent risk measures

Grechuk

Zabarankin

2016

European Journal of Operational Research

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In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or mean-deviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor's preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor's coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari's dual utility. It is solved in single-period and multi-period formulations and is demonstrated in a case study with the FTSE 100 index.

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Section: Propositionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 93%

“…with Q M defined by either (10), (11), or (12), if the agent requires ρ to conform to preference conditions (a), (b), or (c), respectively.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Inverse portfolio problem with coherent risk measures

Grechuk

Zabarankin

2016

European Journal of Operational Research

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“…As with coherent risk measures, investor's deviation measure can be recovered from the rate of return of investor's optimal (preferable) portfolio, see [20].…”

Section: Examples Of Deviation Measures Include Standard Lower Semidementioning

confidence: 99%

Synergy effect of cooperative investment

Grechuk

Zabarankin

2015

Ann Oper Res

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Cooperative investment consists of two problems: finding an optimal cooperative investment strategy and fairly dividing investment outcome among participating agents. In general, the two problems cannot be solved separately. It is known that when agents' preferences are represented by mean-deviation functionals, sharing of optimal portfolio creates instruments that, on the one hand, satisfy individual risk preferences but, on the other hand, are not replicable on an incomplete market, so that each agent is strictly better off in participating in cooperative investment than investing alone. This synergy effect is shown to hold when agents' acceptance sets are represented by cash-invariant utility functions in the case of multiperiod investment with an arbitrary feasible investment set. In this case, a set of all Pareto-optimal allocations is characterized, and an equilibrium-based method for selecting a "fair" Pareto-optimal allocation is suggested. It is also shown that if exists, the "fair" allocation belongs to the core of the corresponding cooperative game. The equilibrium-based method is then extended to the case of arbitrary utility functions. The obtained results are demonstrated in a multiperiod cooperative investment problem with investors imposing drawdown constraints on investment strategies.

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Random Variables

Zabarankin

Uryasev

2013

Statistical Decision Problems

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Inverse portfolio problem with mean-deviation model

Cited by 29 publications

References 15 publications

Inverse portfolio problem with coherent risk measures

Inverse portfolio problem with coherent risk measures

Synergy effect of cooperative investment

Random Variables

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