Risk Measures and Progressive Enlargement of Filtration: A BSDE Approach

Calvia, Alessandro; Gianin, Emanuela Rosazza

doi:10.1137/19m1259134

Cited by 11 publications

(5 citation statements)

References 34 publications

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“…As emphasized by Kalkbrener (2005) in the static case, however, full allocation and no-undercut together with (X ; X ) = ρ(X ) are incompatible for convex risk measures that are not coherent since these axioms together imply subadditivity. Nevertheless, as underlined by Brunnermeier and Cheridito (2019), full allocation can be dropped when, e.g., the CAR is considered only for monitoring purposes [see also Canna et al (2020), Centrone and Rosazza Gianin (2018) and the references therein for a deeper discussion]. For the reason above, sub-allocation and weak convexity can be defined and investigated as alternatives to full allocation.…”

Section: Bsdes and Their Connection To Dynamic Risk Measuresmentioning

confidence: 99%

Dynamic capital allocation rules via BSDEs: an axiomatic approach

Mastrogiacomo

Gianin

2022

Ann Oper Res

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In this paper, we study capital allocation for dynamic risk measures, with an axiomatic approach but also by exploiting the relation between risk measures and BSDEs. Although there is a wide literature on capital allocation rules in a static setting and on dynamic risk measures, only a few recent papers on capital allocation work in a dynamic setting and, moreover, those papers mainly focus on the gradient approach. To fill this gap, we then discuss new perspectives to the capital allocation problem going beyond those already existing in the literature. In particular, we introduce and investigate a general axiomatic approach to dynamic capital allocations as well as an approach suitable for risk measures induced by g-expectations under weaker assumptions than Gateaux differentiability.

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Section: Bsdes and Their Connection To Dynamic Risk Measuresmentioning

confidence: 99%

Dynamic capital allocation rules via BSDEs: an axiomatic approach

Mastrogiacomo

Gianin

2022

Ann Oper Res

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“…Second and somehow related to the previous point, there is a huge literature on risk measures induced by BSDEs in a Brownian setting or in a setting with jumps. See, among others, Barrieu and El Karoui [2], Delbaen et al [17], Rosazza Gianin [33], Laeven and Stadje [26], Quenez and Sulem [31], Calvia and Rosazza Gianin [8]. Finally, some recent works (see Kromer and Overbeck [24,25] and Mabitsela et al [27]) already focus on dynamic risk measures induced by BSDEs and Volterra equations to investigate the gradient allocation.…”

Section: Dynamic Risk Measuresmentioning

confidence: 99%

Dynamic capital allocation rules via BSDEs: an axiomatic approach

Matrogiacomo¹,

Gianin²

2021

Preprint

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In the theory of risk measures, capital allocation is a well-known problem consisting in sharing "ad hoc" the margin required for a position among the different sources of riskiness. Such a problem has been faced in the literature by using different approaches (depending on the nature of the risk measure behind) also in connection with systemic risk and game theory. Although there is a wide literature on the relation between dynamic risk measures and BSDEs and on capital allocation rules in a static setting, only a few recent papers on capital allocation work in a dynamic setting and, moreover, those papers mainly focus on the gradient approach.In this paper, we discuss new perspectives to the capital allocation problem going beyond those already existing in the literature. In particular, we introduce and investigate a general axiomatic approach to dynamic capital allocations as well as an approach suitable for risk measures induced by g-expectations under weaker assumptions than Gateaux differentiability.

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“…Faidi, Matoussi and Mnif (2011) and Faidi, Matoussi and Mnif (2017) investigate the related stochastic control problem by relative entropy and φ-divergences. Laeven and Stadje (2014) and Calvia and Rosazza Gianin (2020) examine the dynamic risk measures and related BSDEs in the jump situation, and the readers can refer to Rosazza Gianin (2006), Jiang (2008) and Delbaen, Peng and Rosazza Gianin (2010) for the Brownian motion case.…”

Section: Introductionmentioning

confidence: 99%

Pricing principle via Tsallis relative entropy in incomplete market

Tian¹

2022

Preprint

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A pricing principle is proposed for non-attainable q-exponential bounded contingent claims in an incomplete Brownian motion market setting. This pricing functional is compatible with prices for attainable claims, and it is defined by the solution of a specific quadratic backward stochastic differential equation (BSDE). Except translation invariance, the pricing principle processes lots of elegant properties, such as monotonicity, time consistency, concavity etc. Tsallis relative entropy theory is found to be closely related to this pricing criterion. The buyer evaluates the contingent claim under the "distorted Radon-Nikodym derivative" and adjustment by Tsallis relative entropy over a family of equivalent martingale measures. The asymptotic behavior of the pricing principle for risk aversion coefficient is also investigated. The pricing functional is proved between minimal martingale measure pricing and conditional certainty equivalence of q-exponential utility.

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Risk Measures and Progressive Enlargement of Filtration: A BSDE Approach

Cited by 11 publications

References 34 publications

Dynamic capital allocation rules via BSDEs: an axiomatic approach

Dynamic capital allocation rules via BSDEs: an axiomatic approach

Dynamic capital allocation rules via BSDEs: an axiomatic approach

Pricing principle via Tsallis relative entropy in incomplete market

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