Stability of utility maximization in nonequivalent markets

Weston, Kimberly

doi:10.1007/s00780-016-0289-z

Cited by 6 publications

(4 citation statements)

References 31 publications

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“…We note that there are stability results in the literature which ensure that if (2.9) holds for some Q ∈ M 1 (P), then it also holds in a neighbourhood around that Q; see e.g. [54,78]. For the case when the infimum and supremum can be interchanged, the set Q can be restricted to measures for which (2.9) holds without affecting the indirect utility; cf.…”

Section: Existence Of An Optimal Strategymentioning

confidence: 99%

Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals

Källblad

2017

Finance Stoch

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Motivated by recent axiomatic developments, we study the risk-and ambiguity-averse investment problem where trading takes place in continuous time over a fixed finite horizon and terminal payoffs are evaluated according to criteria defined in terms of quasiconcave utility functionals. We extend to the present setting certain existence and duality results established for so-called variational preferences by Schied (Finance Stoch. 11:107-129, 2007). The results are proved by building on existing results for the classical utility maximization problem, combined with a careful analysis of the involved quasiconvex and semicontinuous functions.Keywords Model uncertainty · Ambiguity aversion · Quasiconvex risk measures · Optimal investment · Robust portfolio selection · Duality theory

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Section: Existence Of An Optimal Strategymentioning

confidence: 99%

Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals

Källblad

2017

Finance Stoch

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“…Due to the vastness of this literature, we refer the reader to the book by Prigent [51] for references. Finally, in more recent times and starting from the works of Kardaras and Žitković, the stability of utility maximisation has been studied in Kardaras and Žitković [37], Larsen [39], Larsen and Žitković [40], Mocha and Westray [43] and Weston [53], among others.…”

Section: Literaturementioning

confidence: 99%

Adapted Wasserstein distances and stability in mathematical finance

et al. 2020

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Assume that an agent models a financial asset through a measure Q with the goal to price/hedge some derivative or optimise some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, the agent is left with the possibility that Q does not provide an exact description of reality. This leads us to the following question: will the hedge still be somewhat meaningful for models in the proximity of Q? If we measure proximity with the usual Wasserstein distance (say), the answer is No. Models which are similar with respect to the Wasserstein distance may provide dramatically different information on which to base a hedging strategy. Remarkably, this can be overcome by considering a suitable adapted version of the Wasserstein distance which takes the temporal structure of pricing models into account. This adapted Wasserstein distance is most closely related to the nested distance as pioneered by Pflug and Pichler (

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“…Due to the vastness of this literature we refer the reader to the book [54] for references. Finally, in more recent times and starting from the works of Kardaras and Žitković, the stability of utility maximization has been studied in [38,40,41,44,57] among others.…”

Section: Literaturementioning

confidence: 99%

Adapted Wasserstein Distances and Stability in Mathematical Finance

Backhoff-Veraguas¹,

Bartl²,

Beiglböck³

et al. 2019

Preprint

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Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q does not provide an exact description of reality. This leads us the following question: will the hedge still be somewhat meaningful for models in the proximity of Q?If we measure proximity with the usual Wasserstein distance (say), the answer is NO. Models which are similar wrt Wasserstein distance may provide dramatically different information on which to base a hedging strategy.Remarkably, this can be overcome by considering a suitable adapted version of the Wasserstein distance which takes the temporal structure of pricing models into account. This adapted Wasserstein distance is most closely related to the nested distance as pioneered by Pflug and Pichler [49,50,51]. It allows us to establish Lipschitz properties of hedging strategies for semimartingale models in discrete and continuous time. Notably, these abstract results are sharp already for Brownian motion and European call options.

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Stability of utility maximization in nonequivalent markets

Cited by 6 publications

References 31 publications

Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals

Risk- and ambiguity-averse portfolio optimization with quasiconcave utility functionals

Adapted Wasserstein distances and stability in mathematical finance

Adapted Wasserstein Distances and Stability in Mathematical Finance

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