Empirical study on optimal reinsurance for crop insurance in China from an insurer's perspective

This study investigates the optimal reinsurance for crop insurance in China in an insurer＇s perspective using the data from Inner Mongolia, Jilin, and Liaoning, China. On the basis of the loss ratio distributions modeled by An Hua Crop Risk Evaluation System, we use the empirical model developed by Tan and Weng（2014） to study the optimal reinsurance design for crop insurance in China. We find that, when the primary insurer＇s loss function, the principle of the reinsurance premium calculation, and the risk measure are given, the level of risk tolerance of the primary insurer, the safety loading coefficient of the reinsurer, and the constraint on reinsurance premium budget affect the optimal reinsurance design. When a strict constraint on reinsurance premium budget is implemented, which often occurs in reality, the limited stop loss reinsurance is optimal, consistent with the common practice in reality. This study provides suggestions for decision making regarding the crop reinsurance in China. It also provides empirical evidence for the literature on optimal reinsurance from the insurance market of China. This evidence undoubtedly has an important practical significance for the development of China＇s crop insurance.

VAR AND CTE BASED OPTIMAL REINSURANCE FROM A REINSURER'S PERSPECTIVE

In this article,we study optimal reinsurance design.By employing the increasing convex functions as the admissible ceded loss functions and the distortion premium principle,we study and obtain the optimal reinsurance treaty by minimizing the VaR(value at risk)of the reinsurer's total risk exposure.When the distortion premium principle is specified to be the expectation premium principle,we also obtain the optimal reinsurance treaty by minimizing the CTE(conditional tail expectation)of the reinsurer's total risk exposure.The present study can be considered as a complement of that of Cai et al.[5].

Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Optimal Reinsurance Under Distortion Risk Measures and Expected Value Premium Principle for Reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer's risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer's optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.

Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria:Partial and Full Information

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.

Optimal reinsurance designs based on risk measures:a review

Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.

Applications of the Aversion Order of Risks in Reinsurance

The aversion order is a way of ordering of risks. Is there the optimal in aversion order in reinsurance contracts of reinsurance？ This paper discusses these objects and gives some optimal reinsurance contracts in certain sets of feasible reinsurance contracts.

VaR Criteria for optimal limited changeloss and truncated change-loss reinsurance

Reinsurance can provide an effective way for insurer to manage its risk exposure. In this paper, we further analyze the optimal reinsurance models recently proposed by J. Cai and K. S. Tan [Astin Bulletin, 2007, 37（1）： 93- 112]. With the criteria of minimizing the value-at-risk （VaR） risk measure of insurer＇s total loss exposure, we derive the optimal values of sharing proportion a, retention d, and layer 1 of two reinsurance treaties： the limited change- loss f（x） = a{（x - d）＋ - （x -l）＋} and the truncated change-loss f（x） = a（x - d）＋I（x≤t）. Both of the reinsurance plans have been considered to be more realistic and practical in the real business. Our solutions have several appealing features： （i） there is only one condition to verify for the existence of optimal limited change-loss reinsurance while there always exists an optimal truncated change-loss reinsurance, （ii） the resulting optimal parameters have simple analytic forms which depend only on assumed loss distribution, reinsurer＇s safety loading, and insurer＇s risk tolerance, （iii） the optimal retention d for limited change-loss reinsurance is the same as that by Cai and Tan while the optimal value is smaller for truncated change-loss, （iv） the optimal sharing proportion and layer are always the same for both reinsurance plans, （v） minimized VaR are strictly lower than the values derived by Cai and Tan, （vi） the optimization results reveal possible drawbacks of VaR-based risk management that a heavy tail risk exposure may be expressed by lower VaR.

OPTIMAL PROPORTIONAL REINSURANCE UNDER DEPENDENT RISKS

This paper considers a correlated risk model with thinning-dependence structure. The au- thors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and the optimal proportional reinsurance under mean variance principle for the proposed model. The au- thors derive the optimal solutions and the numerical illustrations to show the impact of the dependence among the classes of business on the optimal reinsurance arrangements.

Optimal Investment Problem for an Insurer and a Reinsurer

This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer： The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer＇s optimal investment strategies under the two cases.