Competitive Equilibria in a Comonotone Market

Bilateral Risk Sharing With Heterogeneous Beliefs and Exposure Constraints

“…In the literature on risk sharing, it is common to focus on homogeneous beliefs, and to consider an exogenously given aggregate risk. In such situations, Paretooptimal risk allocations are typically comonotonic with this aggregate risk (e.g., Boonen et al, 2018). This does not allow for betting (e.g., put options) against the aggregate risk.…”

“…For instance, Borch (1962), Wilson (1968), Gerber (1978), Bühlmann and Jewell (1979), Kaluszka (2004), and Aase (1993Aase ( , 2010) study the EU case, while Jouini et al (2008) and Ludkovski and Young (2009) study dual utilities (as in Yaari, 1987), or more generally, law-invariant monetary utility functions. Moreover, Tsanakas and Christofides (2006), Xia and Zhou (2016), Jin et al (2019), and Boonen et al (2018) study the case of RDU. As an exception, Boonen (2017) studies Pareto-optimal risk sharing with both expected and dual utilities.…”

Weighted Comonotonic Risk Sharing Under Heterogeneous Beliefs

“…Moreover, different from previous papers, we assume that each agent is assigned to a fixed weight, and we optimize the weighted sum of distortion risk measures over a set of comonotonic allocations. Comonotonicity of an optimal allocation is a necessary condition for an Arrow-Debreu equilibrium to exist in a complete market; see the discussions in Boonen et al (2018). We are interested in comonotonic allocations also because in the context of insurance, comonotonicity of insurance contracts rules out moral hazard, so that a policyholder will not increase the ground-up loss purposely in order to receive more coverage from an insurer; see, for example, Boonen and Ghossoub (2019).…”

“…If we remove the assumption of comonotonicity, it will be challenging to find an explicit optimal allocation even with value at risk (VaR) and for identical weights under heterogeneous beliefs; see Embrechts et al (2018b). See Boonen et al (2018), Asimit andZhuang et al (2016) for more discussions on the use of comonotonic allocations in risk-sharing games and insurance. Under the assumption of comonotonicity, we are able to find optimal allocations for risk sharing with general distortion risk measures and characterize the set of Pareto-optimal allocations.…”

Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints

“…For instance, Borch (1962), Wilson (1968), Gerber (1978), Bühlmann and Jewell (1979), Kaluszka (2004), and Aase (1993Aase ( , 2010) study the EU case, while Jouini et al (2008) and Ludkovski and Young (2009) study dual utilities (as in Yaari, 1987), or more generally, law-invariant monetary utility functions. Moreover, Tsanakas and Christofides (2006), Xia and Zhou (2016), Jin et al (2019), and Boonen et al (2018) study the case of RDU. As an exception, Boonen (2017) studies Pareto-optimal risk sharing with both expected and dual utilities.…”