Forward Exponential Performances: Pricing and Optimal Risk Sharing

Anthropelos, Michail

doi:10.1137/130910087

Cited by 10 publications

(13 citation statements)

References 40 publications

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“…The above definition assumes the optimizer is attained. This is a somewhat strong assumption which is discussed in [25,1]. There it is argued that such constraint is not necessary for the forward utility construction in certain contexts.…”

Section: Forward Dynamic Utilities (Classic)mentioning

confidence: 99%

“…To cope with the limitation of the backward-in-time view induced by the classical utility optimization formulation, and, to better address this forward view, the mathematical tool of forward utilities was developed. It was initially introduced for the analysis of the portfolio management problems in [20,21,22] and subsequently expanded [25,1,7] and [11,9,10]. The latter dealing with general forward utility Itô random fields and with applications to longevity risk.…”

Section: Introductionmentioning

confidence: 99%

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Forward Utilities and Mean-Field Games Under Relative Performance Concerns

Reis

Платонов

2021

Springer Proceedings in Mathematics &Amp; Statistics

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We introduce the concept of mean field games for agents using Forward utilities to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.

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Section: Forward Dynamic Utilities (Classic)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Forward Utilities and Mean-Field Games Under Relative Performance Concerns

Reis

Платонов

2021

Springer Proceedings in Mathematics &Amp; Statistics

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“…This sounds a very promising and interesting alternative to the approach of PDEs. For the exponential case, we learned from Christoph Frei that, this question was addressed recently by Anthropelos (2013).…”

Section: Conclusion and Related Open Problemsmentioning

confidence: 99%

“…Indeed, forward utilities were used in the context of risk measures in Zariphopoulou and Zitkovic (2010). In Henderson (2007) and Anthropelos (2013), the notion of forward utilities is mainely and extensively used for indifference pricing and/or evaluation. There were many attempts to characterize these forward utilities starting with Berrier, Rogers and Tehrenchi (2009) under strong assumptions on the market models.…”

Section: Introductionmentioning

confidence: 99%

Explicit Description of HARA Forward Utilities and Their Optimal Portfolios

Choulli¹,

Ma²

2017

Theory Probab. Appl.

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This paper deals with forward performances of HARA type. Precisely, for a market model in which stock price processes are modeled by a locally bounded d-dimensional semimartingale, we elaborate a complete and explicit characterization for this type of forward utilities. Furthermore, the optimal portfolios for each of these forward utilities are explicitly described. Our approach is based on the minimal Hellinger martingale densities that are obtained from the important statistical concept of Hellinger process. These martingale densities were introduced recently, and appeared herein tailor-made for these forward utilities. After outlining our parametrization method for the HARA forward, we provide illustrations on discrete-time market models. Finally, we conclude our paper by pointing out a number of related open questions.

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“…As a result, the market (be the original or the fictitious ones) is incomplete. Forward criteria for incomplete markets have been developed before but only when incompleteness comes exclusively from imperfectly correlated stochastic factors affecting the stocks' dynamics (see, among others, [4,40,41,57]). Herein, however, the kind of incompleteness is different, for it is generated by the specialization constraints.…”

Section: Introductionmentioning

confidence: 99%

Competition in Fund Management and Forward Relative Performance Criteria

Anthropelos¹,

Geng²,

Zariphopoulou³

2020

Preprint

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In an Itô-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversification settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria, leading to the respective notions of forward best-response criterion and forward Nash equilibrium. The motivation to develop such criteria comes from the need to relax various crucial, but quite stringent, existing assumptions -such as, the a priori choices of both the market model and the investment horizon, the commonality of the latter for both managers as well as the full a priori knowledge of the competitor's policies for the best-response case. We focus on locally riskless criteria and deduce the random forward equations. We solve the CRRA cases, thus also extending the related results in the classical setting. An important by-product of the work herein is the development of forward performance criteria for investment problems in Itô-diffusion markets under the presence of correlated random endowment process for both the perfectly and the incomplete market cases.

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Forward Exponential Performances: Pricing and Optimal Risk Sharing

Cited by 10 publications

References 40 publications

Forward Utilities and Mean-Field Games Under Relative Performance Concerns

Forward Utilities and Mean-Field Games Under Relative Performance Concerns

Explicit Description of HARA Forward Utilities and Their Optimal Portfolios

Competition in Fund Management and Forward Relative Performance Criteria

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