Risk sharing for capital requirements with multidimensional security markets

Liebrich, Felix-Benedikt; Svindland, Gregor

doi:10.1007/s00780-019-00402-6

Cited by 22 publications

(13 citation statements)

References 47 publications

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“…Existence issues are studied and related concepts of equilibrium are introduced. Recent further extensions have been obtained in Liebrich and Svindland [33].…”

Section: Remark 13mentioning

confidence: 95%

Systemic optimal risk transfer equilibrium

Biagini¹,

Doldi

Fouque

et al. 2021

Math Finan Econ

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We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the Bühlmann’s classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, and Pareto optimality of such a SORTE. In both the Bühlmann and the SORTE definition, each agent is behaving rationally by maximizing his/her expected utility given a budget constraint. The two approaches differ by the budget constraints. In Bühlmann’s definition the vector that assigns the budget constraint is given a priori. On the contrary, in the SORTE approach, the vector that assigns the budget constraint is endogenously determined by solving a systemic utility maximization. SORTE gives priority to the systemic aspects of the problem, in order to optimize the overall systemic performance, rather than to individual rationality.

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“…Existence issues are studied and related concepts of equilibrium are introduced. Recent further extensions have been obtained in Liebrich and Svindland [33].…”

Section: Remark 13mentioning

confidence: 95%

Systemic optimal risk transfer equilibrium

Biagini¹,

Doldi

Fouque

et al. 2021

Math Finan Econ

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“…The former poses a capital adequacy test that the agent attempts to pass with hedging instruments from the security market. These capital requirements follow the spirit of Frittelli & Scandolo [24] and are studied in, e.g., Baes et al [8], Farkas et al [20], and Liebrich & Svindland [31]. They are typically neither law-invariant nor cash-additive functions.…”

Section: Introductionmentioning

confidence: 99%

Risk sharing under heterogeneous beliefs without convexity

Liebrich¹

2021

Preprint

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We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference probability measures. Moreover, individual risk assessments are assumed to be consistent with the respective second-order stochastic dominance relations. We do not assume their convexity though. A simple sufficient condition for the existence of Pareto optima is provided. Its proof combines local comonotone improvement with a Dieudonné-type argument, which also establishes a link of the optimal allocation problem to the realm of "collapse to the mean" results. Finally, we extend the results to capital requirements with multidimensional security markets.

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“…In this case, ρ(X) is the minimal amount of capital that has to be raised at the initial date and invested in a portfolio of eligible assets to reach acceptability. This type of risk measures, which can be viewed as a generalization of superreplication prices, has been studied, e.g., in [Föllmer and Schied, 2002], [Artzner et al, 2009], [Farkas et al, 2015], [Liebrich and Svindland, 2019], [Baes et al, 2020].…”

Section: Introductionmentioning

confidence: 99%

Risk measures beyond frictionless markets

Arduca¹,

Munari²

2021

Preprint

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We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature of our approach is that we embed portfolio constraints and transaction costs into the securities market. As a consequence, we have to dispense with the property of translation invariance, which plays a key role in the classical theory. We provide a comprehensive analysis of relevant properties such as star shapedness, positive homogeneity, convexity, quasiconvexity, subadditivity, and lower semicontinuity. In addition, we establish dual representations for convex and quasiconvex risk measures. In the convex case, the absence of a special kind of arbitrage opportunities allows to obtain dual representations in terms of pricing rules that respect market bid-ask spreads and assign a strictly positive price to each nonzero position in the regulator's acceptance set.

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Risk sharing for capital requirements with multidimensional security markets

Cited by 22 publications

References 47 publications

Systemic optimal risk transfer equilibrium

Systemic optimal risk transfer equilibrium

Risk sharing under heterogeneous beliefs without convexity

Risk measures beyond frictionless markets

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