A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

Bielecki, Tomasz R.; Cialenco, Igor; Pitera, Marcin

doi:10.1186/s41546-017-0012-9

Cited by 31 publications

(44 citation statements)

References 106 publications

(218 reference statements)

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“…Recall that this issue appears already in a uniprior setting, in the study of dynamic risk measures for instance, and is linked to the law of iterated conditional expectations and the dynamic programming principle. We refer to the surveys of Acciaio and Penner (2011) and Bielecki, Cialenco, and Pitera (2016) for detailed overviews. When introducing multiple‐priors one has to be even more careful with time‐consistency.…”

Section: The Modelmentioning

confidence: 99%

Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework

Blanchard¹,

Carassus

2020

Mathematical Finance

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This paper formulates a utility indifference pricing model for investors trading in a discrete time financial market under nondominated model uncertainty. Investor preferences are described by possibly random utility functions defined on the positive axis. We prove that when the investors's absolute risk aversion tends to infinity, the multiple‐priors utility indifference prices of a contingent claim converge to its multiple‐priors superreplication price. We also revisit the notion of certainty equivalent for multiple‐priors and establish its relation with risk aversion.

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Section: The Modelmentioning

confidence: 99%

Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework

Blanchard¹,

Carassus

2020

Mathematical Finance

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“…We remark that the tower-property plays an important role in the theory on dynamic risk measures, see for instance Bielecki et al (2017) for a survey, and refer to Ma et al (2018) for further applications and discussions. The important difference between the portfolio optimization problem we study herein and the setting of Ma et al (2018) is that the Itô process described through the stochastic differential equation 46is given and fixed.…”

Section: Relations With the Dynamic Utility Approachmentioning

confidence: 97%

Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion

Strub

Zariphopoulou

2021

Mathematical Finance

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We introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the timeconsistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes and provide the following dichotomy: it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, 'distorted' measure and a related market. We then build a striking correspondence between the forward

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“…Let us assume that {φ x t } t∈T is weakly acceptance time consistent. Using counterpart of Proposition 4.3 for stochastic processes (see [BCP16]) we get…”

Section: Proof Of Proposition 49mentioning

confidence: 97%

“…This is meant to illustrate the framework developed earlier in this paper. As mentioned in the Introduction, see [BCP16] for a comprehensive survey of various types of time consistency and connections between them. The notion of weak time consistency was introduced in [Tut08], and subsequently studied in [AP11, ADE + 07, CDK06, DS05, AFP12].…”

Section: Weak Time Consistencymentioning

confidence: 99%

A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time

2018

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In this paper we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures (also known as acceptability indices). The proposed framework not only integrates existing forms of time consistency, but also provides a comprehensive toolbox for analysis and synthesis of the concept of time consistency in decision making. In particular, it allows for in depth comparative analysis of (most of) the existing types of time consistency -a feat that has not be possible before and which is done in the companion paper [BCP16] to this one. In our approach the time consistency is studied for a large class of maps that are postulated to satisfy only two properties -monotonicity and locality. The time consistency is defined in terms of an update rule. The form of the update rule introduced here is novel, and is perfectly suited for developing the unifying framework that is worked out in this paper.As an illustration of the applicability of our approach, we show how to recover almost all concepts of weak time consistency by means of constructing appropriate update rules.

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A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective

Cited by 31 publications

References 106 publications

Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework

Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework

Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion

A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time

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