SSRN Author: Mario GhossoubMario Ghossoub SSRN Content
https://www.ssrn.com/author=716876
https://www.ssrn.com/rss/en-usWed, 21 Aug 2019 01:07:43 GMTeditor@ssrn.com (Editor)Wed, 21 Aug 2019 01:07:43 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Budget-Constrained Optimal Retention with an Upper Limit on the Retained LossUnlike sophisticated institutional insurance buyers, individual insurance seekers often use simple heuristic tools for risk management purposes, such as requiring that an insurance arrangement will not result in a retained loss that exceeds a certain predetermined and fixed level. In this paper, we re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss; but we further impose an additional upper-limit constraint on the retained loss and assume that the insurer distorts his subjective probability measure. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. We characterize the optimal ...
https://www.ssrn.com/abstract=3320528
https://www.ssrn.com/1816907.htmlTue, 20 Aug 2019 08:05:15 GMTREVISION: On the Existence of a Representative Reinsurer Under Heterogeneous BeliefsThis paper studies a one-period optimal reinsurance design model with n reinsurers and an insurer. The reinsurers are endowed with expected-value premium principles and with heterogeneous beliefs regarding the underlying distribution of the insurer’s risk. Under general preferences for the insurer, a representative reinsurer is characterized. This means that all reinsurers can be treated collectively by means of a hypothetical premium principle in order to determine the optimal total risk that is ceded to all reinsurers. The optimal total ceded risk is then allocated to the reinsurers by means of an explicit solution. This is shown both in the general case and under the no-sabotage condition that avoids possible ex post moral hazard on the side of the insurer, thereby extending the results of Boonen et al. (2016). We subsequently derive closed-form optimal reinsurance contracts in case the insurer maximizes expected net wealth. Moreover, under the no-sabotage condition, we derive ...
https://www.ssrn.com/abstract=3300773
https://www.ssrn.com/1811456.htmlWed, 31 Jul 2019 15:11:11 GMTREVISION: Optimal Insurance Under Rank-Dependent Expected UtilityWe re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015), Xu (2018), and Xu et al. (2015). Unlike the latter, we do not impose the no sabotage condition on admissible indemnities, that is, the comonotonicity of indemnity functions and retention functions with the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. Hence, monotonicity properties of indemnification schedules become of second-order concern. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2015). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that ...
https://www.ssrn.com/abstract=3230306
https://www.ssrn.com/1778288.htmlTue, 09 Apr 2019 22:49:08 GMTNew: Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure ConstraintsThis paper studies bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility preferences and the other agent has Rank-Dependent Utility preferences with a general probability distortion function. We impose exogenous constraints on the risk exposure for both agents, and we allow for any type or level of belief heterogeneity. We show that Pareto-optimal risk-sharing contracts can be obtained via a constrained utility maximization under a participation constraint of the other agent. This allows us to give an explicit characterization of optimal risk-sharing contracts. In particular, we show that an optimal contract is a monotone function of the likelihood ratio, where the latter is obtained from Lebesgue's Decomposition Theorem.
https://www.ssrn.com/abstract=3345149
https://www.ssrn.com/1773366.htmlSat, 23 Mar 2019 14:38:24 GMTREVISION: Optimal Insurance Without the Nonnegativity Constraint on Indemnities: Ambiguity and Belief HeterogeneityIn Arrow's (1971) classical problem of optimal insurance design, a linear deductible schedule is optimal for an Expected-Utility (EU) maximizing decision maker (DM), if the premium depends on the indemnity's actuarial value, if the DM and the insurer share the same probabilistic beliefs about the realizations of the random loss, and under the classical constraints that, in each state of the world, the indemnity is nonnegative and does not exceed the value of the loss. Raviv (1979) re-examined Arrow's problem and concluded that the presence of a deductible is due to both the nonnegativity constraint on the indemnity and the variability in the cost of insurance. In an effort to test this statement, Gollier (1987) relaxes the nonnegativity constraint and argues that the existence of a deductible is only due to the variability in the cost of insurance. In this paper, we test whether the intuition behind Gollier's result still holds under more general preferences for the DM and the ...
https://www.ssrn.com/abstract=3014934
https://www.ssrn.com/1765426.htmlThu, 21 Feb 2019 09:38:07 GMTREVISION: Budget-Constrained Optimal Insurance with an Upper Limit on the Retained LossUnlike sophisticated institutional insurance buyers, individual insurance seekers often use simple heuristic tools for risk management purposes, such as requiring that an insurance arrangement will not result in a retained loss that exceeds a certain predetermined and fixed level. In this paper, we re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss; but we further impose an additional upper-limit constraint on the retained loss and assume that the insurer distorts his subjective probability measure. We do not impose the no-sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. We characterize the optimal indemnity ...
https://www.ssrn.com/abstract=3320528
https://www.ssrn.com/1764454.htmlSat, 16 Feb 2019 16:20:22 GMTREVISION: Budget-Constrained Optimal Insurance with Belief HeterogeneityWe re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the <i>no sabotage</i> condition on admissible indemnities. Instead, we impose a <i>state-verification cost</i> that the insurer can incur in order to verify the loss severity, which rules out <i>ex post</i> moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a ...
https://www.ssrn.com/abstract=3230312
https://www.ssrn.com/1762750.htmlSun, 10 Feb 2019 23:15:10 GMTREVISION: Budget-Constrained Optimal Insurance with an Upper Limit on the Retained LossUnlike sophisticated institutional insurance buyers, individual insurance seekers often use simple heuristic tools for risk management purposes, such as requiring that an insurance arrangement will not result in a retained loss that exceeds a certain predetermined and fixed level. In this paper, we re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss; but we further impose an additional upper-limit constraint on the retained loss and assume that the insurer distorts his subjective probability measure. We do not impose the no-sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. We characterize the optimal indemnity ...
https://www.ssrn.com/abstract=3320528
https://www.ssrn.com/1762749.htmlSun, 10 Feb 2019 23:12:48 GMTREVISION: Budget-Constrained Optimal Insurance with an Upper Limit on the Retained LossUnlike sophisticated institutional insurance buyers, individual insurance seekers often use simple heuristic tools for risk management purposes, such as requiring that an insurance arrangement will not result in a retained loss that exceeds a certain predetermined and fixed level. In this paper, we re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss; but we further impose an additional upper-limit constraint on the retained loss and assume that the insurer distorts his subjective probability measure. We do not impose the no-sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. We characterize the optimal indemnity ...
https://www.ssrn.com/abstract=3320528
https://www.ssrn.com/1760852.htmlMon, 04 Feb 2019 12:42:43 GMTREVISION: Optimal Insurance Under Rank-Dependent Expected UtilityWe re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015) and Xu et al. (2015). Unlike the latter, we do not impose the no sabotage condition on admissible indemnities, that is, the comonotonicity of indemnity functions and retention functions with the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. Hence, monotonicity properties of indemnification schedules become of second-order concern. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2015). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the ...
https://www.ssrn.com/abstract=3230306
https://www.ssrn.com/1757669.htmlWed, 23 Jan 2019 09:01:05 GMTREVISION: Budget-Constrained Optimal Insurance with Belief HeterogeneityWe re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the <i>no sabotage</i> condition on admissible indemnities. Instead, we impose a <i>state-verification cost</i> that the insurer can incur in order to verify the loss severity, which rules out <i>ex post</i> moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a ...
https://www.ssrn.com/abstract=3230312
https://www.ssrn.com/1757667.htmlWed, 23 Jan 2019 08:57:52 GMTREVISION: On the Existence of a Representative Reinsurer under Heterogeneous BeliefsThis paper studies a one-period optimal reinsurance design model with n reinsurers and an insurer. The reinsurers are endowed with expected-value premium principles and with heterogeneous beliefs regarding the underlying distribution of the insurer's risk. Under general preferences for the insurer, a representative reinsurer is characterized. This means that all reinsurers can be treated collectively by means of a hypothetical premium principle in order to determine the optimal total risk that is ceded to all reinsurers. The optimal total ceded risk is then allocated to the reinsurers by means of an explicit solution. This is shown both in the general case and under the no-sabotage condition that avoids possible ex post moral hazard on the side of the insurer, thereby extending the results of Boonen, Tan, Zhuang (2016). We subsequently derive closed-form optimal reinsurance contracts in case the insurer maximizes expected net wealth. Moreover, under the no-sabotage condition, we ...
https://www.ssrn.com/abstract=3300773
https://www.ssrn.com/1751107.htmlTue, 01 Jan 2019 00:22:58 GMTREVISION: Optimal Insurance Under Rank-Dependent Expected UtilityWe re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015) and Xu et al. (2015). Unlike the latter, we do not impose the no sabotage condition on admissible indemnities, that is, the comonotonicity of indemnity functions and retention functions with the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. Hence, monotonicity properties of indemnification schedules become of second-order concern. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2015). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the ...
https://www.ssrn.com/abstract=3230306
https://www.ssrn.com/1737223.htmlThu, 08 Nov 2018 12:07:24 GMTREVISION: Budget-Constrained Optimal Insurance with Belief HeterogeneityWe re-examine the problem of budget-constrained demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured; and in particular for singularity between these beliefs, that is, disagreement about zero-probability events. We do not impose the <i>no sabotage</i> condition on admissible indemnities. Instead, we impose a <i>state-verification cost</i> that the insurer can incur in order to verify the loss severity, which rules out <i>ex post</i> moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Under a consistency requirement between these beliefs that is weaker than the Monotone Likelihood Ratio (MLR) condition, we characterize the optimal indemnity and show that it has a ...
https://www.ssrn.com/abstract=3230312
https://www.ssrn.com/1737222.htmlThu, 08 Nov 2018 12:06:16 GMTREVISION: Optimal Insurance with Belief HeterogeneityWe re-examine the problem of (budget-constrained) demand for insurance indemnification when the insured and the insurer disagree about the likelihoods associated with the realizations of the insurable loss. For ease of comparison with the classical literature, we adopt the original setting of Arrow (1971), but allow for divergence in beliefs between the insurer and the insured. We do not impose the no sabotage condition on admissible indemnities. Instead, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, which rules out ex post moral hazard issues that could otherwise arise from possible misreporting of the loss by the insured. Moreover, unlike the existing literature, we do not impose conditions on the type or level of disagreement about probabilities, and we allow in particular for singularity between the beliefs, that is, disagreement about zero-probability events. We characterize the optimal indemnity for any type or level of ...
https://www.ssrn.com/abstract=3230312
https://www.ssrn.com/1733290.htmlWed, 24 Oct 2018 23:19:59 GMTREVISION: Optimal Insurance Under Rank-Dependent Expected UtilityWe re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015) and Xu et al. (2015). Unlike the latter, we do not impose the no sabotage condition on admissible indemnities, that is, the comonotonicity of indemnity functions and retention functions with the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2015). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the insured, and we provide a characterization of the optimal retention in that case.
https://www.ssrn.com/abstract=3230306
https://www.ssrn.com/1718128.htmlWed, 22 Aug 2018 20:06:25 GMTREVISION: Optimal Insurance Without the Nonnegativity Constraint on Indemnities: Ambiguity and Belief HeterogeneityIn Arrow's (1971) classical problem of optimal insurance design, a linear deductible schedule is optimal for an Expected-Utility (EU) maximizing decision maker (DM), if the premium depends on the indemnity's actuarial value, if the DM and the insurer share the same probabilistic beliefs about the realizations of the random loss, and under the classical constraints that, in each state of the world, the indemnity is nonnegative and does not exceed the value of the loss. Raviv (1979) re-examined Arrow's problem and concluded that the presence of a deductible is due to both the nonnegativity constraint on the indemnity and the variability in the cost of insurance. In an effort to test this statement, Gollier (1987) relaxes the nonnegativity constraint and argues that the existence of a deductible is only due to the variability in the cost of insurance. In this paper, we test whether the intuition behind Gollier's result still holds under more general preferences for the DM and the ...
https://www.ssrn.com/abstract=3014934
https://www.ssrn.com/1718112.htmlWed, 22 Aug 2018 19:24:41 GMT