On admissible strategies in robust utility maximization

Owari, Keita

doi:10.1007/s11579-012-0068-3

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…We note that allowing negative wealth usually complicates the choice of an appropriate set of admissible strategies yielding the existence of an optimiser; cf. [59,62]. This is not a concern for us since we do not require the existence of a primal optimiser, and hence, without loss of generality, we can restrict to the set of bounded wealth processes.…”

Section: Dual Characterisation Of Robust Forward Criteriamentioning

confidence: 99%

Dynamically consistent investment under model uncertainty: the robust forward criteria

2018

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We combine forward investment performance processes and ambiguityaverse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences.We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107-129, 2007) and Žitković (Ann. Appl. Probab. 19:2176-2210). We also study in detail the so-called timemonotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of riskλ and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated withλ and with the leverage being proportional to the investor's confidence in her estimate. Keywords

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Section: Dual Characterisation Of Robust Forward Criteriamentioning

confidence: 99%

Dynamically consistent investment under model uncertainty: the robust forward criteria

2018

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“…What usually becomes more complex when allowing for negative wealth, is the definition of an appropriate set of admissible strategies yielding the existence of an optimizer 3 (cf. [68,70]). However, as argued above, for the present purposes it suffices to restrict to the set of bounded wealth processes A bd .…”

Section: Self-generation In the Dual Domainmentioning

confidence: 99%

Time-Consistent Investment Under Model Uncertainty: The Robust Forward Criteria

2013

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We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification as well as in preferences and investment horizon specification. It describes the evolution of dynamically-consistent ambiguity averse preferences.We first focus on establishing dual characterizations of the robust forward criteria. This is advantageous as the dual problem amounts to a search for an infimum whereas the primal problem features a saddle-point. Our approach is based on ideas developed in Schied [71] anď Zitković [79]. We then study in detail non-volatile criteria. In particular, we solve explicitly the example of an investor who starts with a logarithmic utility and applies a quadratic penalty function. The investor builds a dynamic estimate of the market price of riskλ and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated withλ. The leverage is proportional to the investor's confidence in her estimateλ.

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“…Here we just give a criterion in terms of "integrabilities" of D and B for the duality without singular term as well as its explicit form when U is finite on R. It constitutes a half of what we call the martingale duality method (see e.g. [2,25,3] for the other half in the classical case and [18] 1 for a partial result in the robust case). For the case dom(U) = R + , see [26] when D, B are constants; [27] with bounded B, and [9] for dom(U) = R with constant D, B; see also [10] for more thorough references.…”

Section: Examples Of "Nice" Integrands and Robust Utility Maximizationmentioning

confidence: 99%

A Robust Version of Convex Integral Functionals

Owari

2013

Preprint

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We study the pointwise supremum of convex integral functionalswhere f : Ω × R → R is a proper normal convex integrand, γ is a proper convex function on the set of probability measures absolutely continuous w.r.t. P, and the supremum is taken over all such measures. We give a pair of upper and lower bounds for the conjugate of I f,γ as direct sums of a common regular part and respective singular parts; they coincide when dom(γ) = {P} as Rockafellar's classical result, while both inequalities can generally be strict. We then investigate when the conjugate eliminates the singular measures, which a fortiori yields the equality in bounds, and its relation to other finer regularity properties of the original functional and of the conjugate.

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On admissible strategies in robust utility maximization

Cited by 3 publications

References 21 publications

Dynamically consistent investment under model uncertainty: the robust forward criteria

Dynamically consistent investment under model uncertainty: the robust forward criteria

Time-Consistent Investment Under Model Uncertainty: The Robust Forward Criteria

A Robust Version of Convex Integral Functionals

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