Download or read book Optimal Reinsurance with Multiple Reinsurers written by Tim J. Boonen and published by . This book was released on 2018 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study economic pricing of reinsurance contracts via competition of an insurer with multiple reinsurers. All firms are endowed with distortion risk measures or expected exponential utilities. We require that contracts are Pareto optimal, individually rational, and satisfy a competition constraint that we call coalition stability. Indemnities are characterized by imposing Pareto optimality, as studied in the literature. In this paper, we characterize the corresponding premiums. There is a gain for the insurer due to the competition constraint. When the firms use distortion risk measures, this constraint yields stability for subcoalitions, which is a condition akin to the core in cooperative game theory. We show this gain for the insurer in closed form. Then, we derive that the premium is represented by a distortion premium function. If the firms use expected exponential utilities, the premium is represented by an exponential premium. We illustrate this premium function with the Mean Conditional Value-at-Risk.
Download or read book Optimal Reinsurance with One Insurer and Multiple Reinsurers written by Tim J. Boonen and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider a one-period optimal reinsurance design model with n reinsurers and an insurer. For very general preferences of the insurer, we obtain that there exists a very intuitive pricing formula for all reinsurers that use a distortion premium principle. The insurer determines its optimal risk that it wants to reinsure via this pricing formula. This risk it wants to reinsure is then shared by the reinsurers via tranching. The optimal ceded loss functions among multiple reinsurers are derived explicitly under the additional assumptions that the insurer's preferences are given by an inverse-S shaped distortion risk measure and that the reinsurer's premium principles are some functions of the Conditional Value-at-Risk. We also demonstrate that under some prescribed conditions, it is never optimal for the insurer to cede its risk to more than two reinsurers.
Download or read book Optimal Reinsurance in a Market of Multiple Reinsurers Under Law Invariant Convex Risk Measures written by Jun Cai and published by . This book was released on 2017 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is natural to connect reinsurance problems with risk measures since a reinsurance contract is an efficient risk management tool for an insurer and the reinsurance premium can also be viewed as a measure of a reinsurer's risk. In this paper, we assume that the insurer uses a law-invariant convex risk measure, while reinsurers use a Wang's premium principle to determine their premiums. We study an optimal reinsurance policy design from an insurer's perspective in a market of multiple reinsurers. Both the insurer's risk measure and the reinsurer's premium principle represent broad families of risk measures with considerable generality. We provide a general formula for the optimal solution which recovers existing results if particular law-invariant convex measures, such as the AVaR, and particular premium principles are assigned.
Download or read book Optimal Reinsurance Arrangements in the Presence of Two Reinsurers written by Yichun Chi and published by . This book was released on 2016 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate the optimal form of reinsurance from the perspective of an insurer when he decides to cede part of the loss to two reinsurers, where the first reinsurer calculates the premium by expected value principle while the premium principle adopted by the second reinsurer satisfies three axioms: distribution invariance, risk loading and preserving stop-loss order. In order to exclude the moral hazard, a typical reinsurance treaty assumes that both the insurer and reinsurers are obligated to pay more for the larger loss. Under the criterion of minimizing value at risk(VaR) or conditional value at risk(CVaR) of the insurer's total risk exposure, we show that an optimal reinsurance policy is to cede two adjacent layers, where the upper layer is distributed to the first reinsurer. To further illustrate the applicability of our results, we derive explicitly the optimal layer reinsurance by assuming a generalized Wang's premium principle for the second reinsurer.
Download or read book Risk Measures and Optimal Reinsurance written by Fangda Liu and published by . This book was released on 2015 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study the optimal reinsurance design problem and extend the classical model in three different directions: (1) In the first framework, we add the additional assumption that the reinsurer can default on its obligations. If the indemnity is beyond the reinsurer's payment ability, the reinsurer fails to pay for the exceeding part and this induces a default risk for the insurer. In our model, the reinsurer is assumed to measure the risk of an insured loss by Value-at-Risk regulation and prepares the same amount of money as the initial reserve. As soon as the indemnity is larger than this value plus the premium, default occurs. From the insurer's point of view, two optimization problems are going to be considered when the insurer: 1) maximizes his expectation of utility; 2) minimizes the VaR of his retained loss. (2) In the second framework, the reinsurance buyer (insurer) adopts a convex risk measure to control his total loss while the reinsurance seller (reinsurer) price the reinsurance contract by Wang's premium principle with a distortion. Without specifying a particular convex risk measure and distortion, we obtain a general expression for the optimal reinsurance contract that minimizes the insurer's total risk exposure. (3) In the third framework, we study optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs. We develop optimal reinsurance contracts that minimize the convex combination of the VaR risk measures of the insurer's loss and the reinsurer's loss under two types of constraints, respectively. The constraints describe the interest of both the insurer and the reinsurer. With the first type of constraints, the insurer and the reinsurer each have their limit on the VaR of their own loss. With the second type of constraints, the insurer has a limit on the VaR of his loss while the reinsurer has a target on his profit from selling a reinsurance contract. For both types of constraints, we derive the optimal reinsurance form for a wide class of reinsurance policies and under the expected value reinsurance premium principle.
Download or read book Optimal Reinsurance written by Ka-Chun Joseph Sung and published by Open Dissertation Press. This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Optimal Reinsurance: a Contemporary Perspective" by Ka-chun, Joseph, Sung, 宋家俊, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In recent years, general risk measures have played an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance problems using risk measures as yard sticks beyond the classical expected utility framework. In this thesis, the stop-loss reinsurance is first shown to be an optimal contract under law-invariant convex risk measures via a new simple geometric argument. This similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution in these cases. These two results hint that law-invariant convex risk measure may be better and more robust to expected larger claims than Value at Risk and Conditional Tail Expectation even though they are more commonly used. In addition, the problem of optimal reinsurance design for a basket of n insurable risks is studied. Without assuming any particular dependence structure, a minimax optimal reinsurance decision formulation for the problem has been successfully proposed. To solve it, the least favorable dependence structure is first identified, and then the stop-loss reinsurances are shown to minimize a general law-invariant convex risk measure of the total retained risk. Sufficient condition for ordering the optimal deductibles are also obtained. Next, a Principal-Agent model is adopted to describe a monopolistic reinsurance market with adverse selection. Under the asymmetry of information, the reinsurer (the principal) aims to maximize the average profit by selling a tailor-made reinsurance to every insurer (agent) from a (huge) family with hidden characteristics. In regard to Basel Capital Accord, each insurer uses Value at Risk as the risk assessment, and also takes the right to choose different risk tolerances. By utilizing the special features of insurance layers, their optimality as the first-best strategy over all feasible reinsurances is proved. Also, the same optimal reinsurance screening problem is studied under other subclass of reinsurances: (i) deductible contracts; (ii) quota-share reinsurances; and (iii) reinsurance contracts with convex indemnity, with the aid of indirect utility functions. In particular, the optimal indirect utility function is shown to be of the stop-loss form under both classes (i) and (ii); while on the other hand, its non-stop-loss nature under class (iii) is revealed. Lastly, a class of nonzero-sum stochastic differential reinsurance games between two insurance companies is studied. Each insurance company is assumed to maximize the difference of the opponent's terminal surplus from that of its own by properly arranging its reinsurance schedule. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer-Lundberg approximation. It is a diffusion risk process with coefficients being modulated by both a continuous-time finite-state Markov Chain and another diffusion process; and correlations among these surplus processes are allowed. In contrast to the tradit
Download or read book Optimal Reinsurance in the Presence of Counterparty Default Risk written by Alexandru Vali Asimit and published by . This book was released on 2014 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The optimal reinsurance arrangement is identified whenever the reinsurer counterparty default risk is incorporated in a one-period model. Our default risk model allows the possibility for the reinsurer to fail paying in full the promised indemnity, whenever it exceeds the level of regulatory capital. We also investigate the change in the optimal solution if the reinsurance premium recognises or not the default in payment. Closed form solutions are elaborated when the insurer's objective function is set via some well-known risk measures. It is also discussed the effect of reinsurance over the policyholder welfare. If the insurer is Value-at-Risk regulated, then the reinsurance does not increase the policyholder's exposure for any possible reinsurance transfer, even if the reinsurer may default in paying the promised indemnity. Numerical examples are also provided in order to illustrate and conclude our findings. It is found that the optimal reinsurance contract does not usually change if the counterparty default risk is taken into account, but one should consider this effect in order to properly measure the policyholders's exposure. In addition, the counterparty default risk may change the insurer's ideal arrangement if the buyer and seller have very different views on the reinsurer's recovery rate.
Download or read book Optimal Reinsurance Analysis from a Crop Insurer s Perspective written by Lysa Porth and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Purpose - The primary objective of this paper is to analyze the optimal reinsurance contract structure from the crop insurer's perspective. Design/Methodology/Approach - A very powerful and flexible empirical-based reinsurance model is used to analyze the optimal form of the reinsurance treaty. The reinsurance model is calibrated to unique data sets including private reinsurance experience for Manitoba, and loss cost ratio experience for all of Canada, under the assumption of the standard deviation premium principle and conditional tail expectation risk measure. Findings - The Vasicek distribution is found to provide the best statistical fit for the Canadian LCR data, and the empirical reinsurance model stipulates that a layer reinsurance contract structure is optimal, which is consistent with market practice. Research Limitations/Implications - While the empirical reinsurance model is able to reproduce the optimal shape of the reinsurance treaty, the model produces some inconsistencies between the implied and observed attachment points. Future research will continue to explore the reinsurance model that will best recover the observed market practice. Practical Implications - Private reinsurance premiums can account for a significant portion of a crop insurer's budget, therefore, this study should be useful for crop insurance companies to achieve efficiencies and improve their risk management. Originality/Value - To the best of our knowledge, this is the first paper to show how a crop insurance firm can optimally select a reinsurance contract structure that minimizes its total risk exposure, considering the total losses retained by the insurer, as well as the reinsurance premium paid to private reinsurers.
Download or read book Pareto Optimal Reinsurance Arrangements Under General Model Settings written by Jun Cai and published by . This book was released on 2016 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. From the purpose of practice, we use numerical examples to show how to determine the best Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer's aim and the reinsurer's goal can be met under the best Pareto-optimal reinsurance contracts.
Download or read book Optimal Reinsurance Policies When the Interests of Both the Cedent and the Reinsurer are Taken Into Account written by Wenjun Jiang and published by . This book was released on 2018 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal forms of reinsurance policies have been studied for a long time in actuarial literature. Most existing results are from the insurer's point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement which might be very attractive to one party (e.g., insurer) can be quite unacceptable to the other party (e.g., reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party's risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaRs of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.
Download or read book Optimization of Excess of Loss Reinsurance Structure written by Mai Muhtaseb and published by . This book was released on 2016 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In the current practice in the region, before purchasing a reinsurance contract, small to medium insurance companies rarely conduct internal analysis of their data and experiences in order to evaluate and achieve optimal reinsurance arrangements and contracts. Most companies settle their reinsurance agreements through reinsurance intermediary, broker, who acts as the link of communication, negotiation and settlement between both the reinsurers and the ceding insurer. Alternatively, the reinsurance companies or intermediaries evaluate and analyze the insurer’s historical losses and offer reinsurance agreement and proposal accordingly. Therefore, the proposed reinsurance structure is not necessarily the insurer’s optimal arrangement. In this thesis, excess of loss reinsurance optimization models are developed in order to enable insurers to utilize user-friendly and efficient tools to evaluate the optimal reinsurance arrangement depending on financial requirements, and to gain better value of their reinsurance contracts. The models are developed to define the insurer’s optimal reinsurance retention and ceding limits for two objectives; minimizing insurer’s retention variance and maximizing insurer’s return on capital. The model maximizing the return on capital resulted in more realistic optimization solutions of retention limits. A sensitivity analysis to evaluate the impact of the model’s parameters on the return on capital was also conducted, and it was concluded that the impact of the insurer’s retention limit on the return on capital was significantly small. Moreover, the defined capital and gross premium safety loading had a major impact on the behavior of the return on capital."--Abstract.
Download or read book An Option Based Approach to Determining the Optimal Reinsurance Stop Loss Premium written by Jorge L. Urrutia and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper uses option-pricing theory to develop a model for determining the optimal reinsurance premium to be charged by the reinsurer to the primary insurer in a nonproportional stop-loss reinsurance treaty. A discussion of several reinsurance contracts is also presented. It is found that the fair reinsurance premium is given by the weighted sum of the level of claims plus the present value of the maximum payoff to the reinsured less the present value of the reinsured's retention limit. The fair reinsurance premium increases in the maximum amount to be paid by the reinsurer, decreases in the retention limit, and is nonmonotonic in the volatility of underlying claims.
Download or read book Optimal Reinsurance Designs written by Chengguo Weng and published by . This book was released on 2009 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research on optimal reinsurance design dated back to the 1960's. For nearly half a century, the quest for optimal reinsurance designs has remained a fascinating subject, drawing significant interests from both academicians and practitioners. Its fascination lies in its potential as an effective risk management tool for the insurers. There are many ways of formulating the optimal design of reinsurance, depending on the chosen objective and constraints. In this thesis, we address the problem of optimal reinsurance designs from an insurer's perspective. For an insurer, an appropriate use of the reinsurance helps to reduce the adverse risk exposure and improve the overall viability of the underlying business. On the other hand, reinsurance incurs additional cost to the insurer in the form of reinsurance premium. This implies a classical risk and reward tradeoff faced by the insurer. The primary objective of the thesis is to develop theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a number of reinsurance models are developed and their optimal reinsurance treaties are derived explicitly. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the most common risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer's profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer's empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.
Download or read book On Pareto Optimal Reinsurance with Constraints Under Distortion Risk Measures written by Wenjun Jiang and published by . This book was released on 2017 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the Pareto-optimal reinsurance policies, where both the insurer's and the reinsurer's risks and returns are considered. We assume that the risks of the insurer and the reinsurer, as well as the reinsurance premium, are determined by some distortion risk measures with different distortion operators. Under the constraint that a reinsurance policy is feasible only if the resulting risk of each party is below some pre-determined values, we derive explicit expressions for the optimal reinsurance polices. Methodologically, we show that the generalized Neyman-Pearson method, the Lagrange multiplier method, and the dynamic control methods can be utilized to solve the optimization problem with constraints. Special cases when both parties' risks are measured by Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are studied in great details. Numerical examples are provided to illustrate practical implications of the results.
Download or read book Reinsurance written by Hansjörg Albrecher and published by John Wiley & Sons. This book was released on 2017-11-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.
Download or read book Pareto optimal Reinsurance Policies with Maximal Synergy written by Wenjun Jiang and published by . This book was released on 2019 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal reinsurance policies have been studied extensively in the economics and insurance literature. Two types of optimality criteria are commonly used: maximizing the expected utility (EU) or minimizing risks. Understandably, applying the two types of criteria usually will result in different “optimal” policies. To strike a balance between maximizing utility and minimizing risk, Borch (1960b) derived the EU-maximizing reinsurance policies assuming that the admissible policies are those that minimize the total variance of the losses borne by the two parties. This in fact implies that only quota-share policies are admissible and greatly simplifies the problem. In this paper, we follow the approach in Borch (1960b). However, we assume that the two parties apply distortion risk measures instead of variance. We first identify a set of reinsurance policies that minimize the total risk shared by the two parties, then we take this set of policies as admissible and determine the Pareto-optimal policies that maximize the EU of the two parties. In contrast to the results in Borch (1960b), we show that applying risk measures such as the Value at Risk (VaR) and the Tail Value at Risk (TVaR) results in multi-layered policies.
Download or read book An Introduction to Mathematical Risk Theory written by Hans U. Gerber and published by . This book was released on 1979 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
