SSRN Author: Tim J. BoonenTim J. Boonen SSRN Content
https://privwww.ssrn.com/author=2363915
https://privwww.ssrn.com/rss/en-usTue, 10 Aug 2021 01:13:39 GMTeditor@ssrn.com (Editor)Tue, 10 Aug 2021 01:13:39 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Optimal Reinsurance with Multiple Reinsurers: Competitive Pricing and Coalition StabilityThis paper studies economic pricing of reinsurance contracts via competition of an insurer with multiple reinsurers. All firms are assumed to be endowed with distortion risk measures or expected exponential utilities. Reinsurance contracts are required to be Pareto optimal, individually rational, and satisfy a competition constraint that we call coalition stability. As shown in the literature, it holds that Pareto optimality is equivalent to a structure on the indemnities. This paper characterizes the corresponding premiums by a competition argument. The competition among reinsurers imposes constraints on the premiums that the reinsurers are able to charge and this may lead to a strictly positive profit for the insurer. When the firms use distortion risk measures, this constraint yields stability for sub-coalitions, which is a condition akin to the core in cooperative game theory. The premiums and the profit of the insurer are derived in closed-form. This paper illustrates this ...
https://privwww.ssrn.com/abstract=3143224
https://privwww.ssrn.com/2048850.htmlMon, 09 Aug 2021 10:56:13 GMTNew: Pareto-optimal Reinsurance with Default Risk and Solvency RegulationThis paper studies an optimal reinsurance problem of Pareto-optimality when the contract is subject to default of the reinsurer. We assume that the reinsurer can invest a share of its wealth in a risky asset and default occurs when the reinsurer's end-of-period wealth is insufficient to cover the indemnity. We show that without the solvency regulation, the optimal indemnity function is of excess-of-loss form, regardless of the investment decision. We model solvency regulation as a constraint on the probability of default. Under solvency regulation, by assuming the investment decision remains the same as in the unconstrained solution, the optimal indemnity function is derived element-wisely. Partial results are given when the indemnity function and investment decision are jointly constrained by the solvency regulation. Numerical examples are provided to illustrate the implications of our results and the sensitivity of the solutions to the model parameters.
https://privwww.ssrn.com/abstract=3775195
https://privwww.ssrn.com/2003194.htmlTue, 16 Mar 2021 17:46:42 GMTREVISION: Risk Sharing with Multiple Indemnity EnvironmentsOptimal risk sharing arrangements have been substantially studied in the literature, from the aspects of generalizing objective functions, incorporating more business constraints, and investigating different optimality criteria. This paper proposes an insurance model with multiple risk environments. We study the case where the two agents are endowed with the Value-at-Risk or the Tail Value-at-Risk, or when both agents are risk-neutral but have heterogeneous beliefs regarding the underlying probability distribution. We show that layer-type indemnities, within each risk environment, are Pareto optimal, which may be environment-specific. From Pareto optimality, we get that the premium can be chosen in a given interval, and we propose to allocate the gains from risk sharing equally between the buyer and seller.
https://privwww.ssrn.com/abstract=3616746
https://privwww.ssrn.com/1999283.htmlMon, 08 Mar 2021 09:46:49 GMTNew: Risk-Sharing and Contingent Premia in the Presence of Systematic Risk: The Case Study of the UK COVID-19 Economic LossesMotivated by macroeconomic risks, such as the COVID-19 pandemic, we consider different risk management platforms and study efficient insurance schemes in the presence of systematic events. More precisely, we consider three platforms: the risk-sharing, insurance and market platform. First, we show that under a non-discriminatory insurance assumption, it is optimal for everybody to bear the average final wealth. This gives rise to a new concept of a contingent premium which collects the premia ex-post after the losses are realised. As a result, an efficient solution is generated in the risk-sharing platform where insurance is a mechanism to redistribute the wealth. Second, we show that in an insurance platform, where the insurance is regulated, we see that there is a need for a social insurance scheme to bear the risk of the tail events. Third, in a competitive market we see how a classical solution can raise the risk of insolvency and in a decentralised market the equilibrium cannot ...
https://privwww.ssrn.com/abstract=3795941
https://privwww.ssrn.com/1998093.htmlThu, 04 Mar 2021 10:17:54 GMTREVISION: Risk Sharing with Multiple Indemnity EnvironmentsOptimal risk sharing arrangements have been substantially studied in the literature, from the aspects of generalizing objective functions, incorporating more business constraints, and investigating different optimality criteria. This paper proposes an insurance model with multiple risk environments. We study the case where the two agents are endowed with the Value-at-Risk or the Tail Value-at-Risk, or when both agents are risk-neutral but have heterogeneous beliefs regarding the underlying probability distribution. We show that layer-type indemnities, within each risk environment, are Pareto optimal, which may be environment-specific. From Pareto optimality, we get that the premium can be chosen in a given interval, and we propose to allocate the gains from risk sharing equally between the buyer and seller.
https://privwww.ssrn.com/abstract=3616746
https://privwww.ssrn.com/1993748.htmlMon, 22 Feb 2021 10:46:07 GMTREVISION: Pricing in a Competitive Stochastic Insurance MarketThis paper studies a one-period stochastic game to determine the optimal premium strategies of non-life insurers in a competitive market. Specifically, the optimal premium strategy is determined by the Nash equilibrium of an n-player game, in which each player is assumed to maximise the expected utility of terminal wealth. The terminal wealth is stochastic, since the number of policies and the size of claims are considered to be random variables. The total loss of each insurer is described by the collective risk model. The expected number of policies is affected by the all premiums in the market and further investigated by two distinct demand functions. Both models have an exponential functional form, that is characterized by market and price sensitivity parameters. The demand in the first model is zero for premiums above a given threshold, whereas the second model does not include such restriction. The pure strategy Nash equilibrium premiums are given as solutions to constrained ...
https://privwww.ssrn.com/abstract=3685009
https://privwww.ssrn.com/1985300.htmlThu, 28 Jan 2021 09:00:59 GMTREVISION: Pricing in a Competitive Stochastic Insurance MarketThis paper studies a one-period stochastic game to determine the optimal premium strategies of non-life insurers in a competitive market. Specifically, the optimal premium strategy is determined by the Nash equilibrium of an n-player game, in which each player is assumed to maximise the expected utility of terminal wealth. The terminal wealth is stochastic, since the number of policies and the size of claims are considered to be random variables. The total loss of each insurer is described by the collective risk model. The expected number of policies is affected by the all premiums in the market and further investigated by two distinct demand functions. Both models have an exponential functional form, that is characterized by market and price sensitivity parameters. The demand in the first model is zero for premiums above a given threshold, whereas the second model does not include such restriction. The pure strategy Nash equilibrium premiums are given as solutions to constrained ...
https://privwww.ssrn.com/abstract=3685009
https://privwww.ssrn.com/1979196.htmlMon, 11 Jan 2021 10:02:58 GMTREVISION: Risk Sharing with Multiple Indemnity EnvironmentsOptimal risk sharing arrangements have been substantially studied in the literature, from the aspects of generalizing objective functions, incorporating more business constraints, and investigating different optimality criteria. This paper proposes an insurance model with multiple risk environments. We study the case where the two agents are endowed with the Value-at-Risk or the Tail Value-at-Risk, or when both agents are risk-neutral but have heterogeneous beliefs regarding the underlying probability distribution. We show that layer-type indemnities, within each risk environment, are Pareto optimal, which may be environment-specific. From Pareto optimality, we get that the premium can be chosen in a given interval, and we propose to allocate the gains from risk sharing equally between the buyer and seller.
https://privwww.ssrn.com/abstract=3616746
https://privwww.ssrn.com/1969639.htmlTue, 08 Dec 2020 10:17:13 GMTNew: Optimal Insurance under Maxmin Expected UtilityWe examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the Maxmin-Expected Utility model of Gilboa and Schmeidler (1989), whereas the insurer is a (risk-averse or risk-neutral) Expected-Utility maximizer. We characterize optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, marginal utility of wealth, belief heterogeneity, as well as ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how the singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several ...
https://privwww.ssrn.com/abstract=3711743
https://privwww.ssrn.com/1965887.htmlFri, 27 Nov 2020 23:50:38 GMTREVISION: Pricing in a Competitive Stochastic Insurance MarketThis paper studies a one-period stochastic game to determine the optimal premium strategies of non-life insurers in a competitive market. Specifically, the optimal premium strategy is determined by the Nash equilibrium of an n-player game, in which each player is assumed to maximise the expected utility of terminal wealth. The terminal wealth is stochastic, since the number of policies and the size of claims are considered to be random variables. The total loss of each insurer is described by the collective risk model. The expected number of policies is affected by the all premiums in the market and further investigated by two distinct demand functions. Both models have an exponential functional form, that is characterized by market and price sensitivity parameters. The demand in the first model is zero for premiums above a given threshold, whereas the second model does not include such restriction. The pure strategy Nash equilibrium premiums are given as solutions to constrained ...
https://privwww.ssrn.com/abstract=3685009
https://privwww.ssrn.com/1953570.htmlTue, 20 Oct 2020 15:53:17 GMTREVISION: Static and Dynamic Risk Capital Allocations With the Euler RuleRisk capital allocations are of central importance in performance measurement. A popular solution concept in the academic literature is the Euler rule. This paper studies the volatility of the Euler rule for capital allocation in static and dynamic empirical applications with a simulated history. The Euler rule is not continuous in small changes of the underlying risk capital allocation problem, and we show that the Euler rule in combination with the Value-at-Risk is very sensitive to empirical measurement error. The use of a known distribution with estimated parameters helps to reduce this error. The Euler rule with an Expected Shortfall risk measure is less volatile, but still more volatile than the proportional rule.
https://privwww.ssrn.com/abstract=3288592
https://privwww.ssrn.com/1953263.htmlTue, 20 Oct 2020 09:01:32 GMTNew: Insurance With Heterogeneous PreferencesThis paper studies an optimal insurance problem with finitely many potential policyholders. A monopolistic, risk-neutral insurer offers an insurance contract, and exponential utility maximizing individuals accept the offer or not. We allow for heterogeneity in the preferences of the individuals, while the insurer cannot discriminate in the insurance premium. We show that it is optimal for the insurer to offer only a full insurance contract, and the price optimization problem is reduced to a discrete problem, where the premium is an indifference premium for one individual in the market. Moreover, if individuals can self-select their insurance coverage given the market premium rate, then we find that partial insurance is generally optimal. Since the risk aversion parameters of individuals is generally unobserved, we also present a simulation-based framework. We show its convergence, and provide numerical examples.
https://privwww.ssrn.com/abstract=3677285
https://privwww.ssrn.com/1948829.htmlWed, 07 Oct 2020 20:04:55 GMTREVISION: Competitive Equilibria in a Comonotone MarketWe investigate competitive equilibria in a special type of incomplete markets, referred to as a comonotone market, where agents can only trade such that their risk allocation is comonotonic. The comonotone market is motivated by the no-sabotage condition. For instance, in a standard insurance market, the allocation of risk among the insured, the insurer and the reinsurers is assumed to be comonotonic a priori to the risk-exchange. Two popular classes of preferences in risk management and behavioral economics, dual utilities (DU) and rank-dependent expected utilities (RDU), are used to formulate agents’ objectives. We present various results on properties and characterization of competitive equilibria in this framework, and in particular their relation to complete markets. For DU-comonotone markets, we find the equilibrium in closed form and for RDU-comonotone markets, we find the equilibrium in closed form in special cases. The fundamental theorems of welfare economics are ...
https://privwww.ssrn.com/abstract=3091424
https://privwww.ssrn.com/1946836.htmlThu, 01 Oct 2020 09:13:01 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://privwww.ssrn.com/abstract=3300773
https://privwww.ssrn.com/1933799.htmlThu, 20 Aug 2020 08:27:11 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://privwww.ssrn.com/abstract=3300773
https://privwww.ssrn.com/1933705.htmlThu, 20 Aug 2020 07:39:28 GMT