Reinsurance Strategy Research Articles

On penalized goal-reaching probability minimization under borrowing and short-selling constraints

Abstract We consider a robust optimal investment–reinsurance problem to minimize the goal-reaching probability that the value of the wealth process reaches a low barrier before a high goal for an ambiguity-averse insurer. The insurer invests its surplus in a constrained financial market, where the proportion of borrowed amount to the current wealth level is no more than a given constant, and short-selling is prohibited. We assume that the insurer purchases per-claim reinsurance to transfer its risk exposure to a reinsurer whose premium is computed according to the mean–variance premium principle. Using the stochastic control approach based on the Hamilton–Jacobi–Bellman equation, we derive robust optimal investment–reinsurance strategies and the corresponding value functions. We conclude that the behavior of borrowing typically occurs with a lower wealth level. Finally, numerical examples are given to illustrate our results.

Optimal reinsurance with multivariate risks and dependence uncertainty

In this paper, we study the optimal reinsurance design from the perspective of an insurer with multiple lines of business, where the reinsurance is purchased by the insurer for each line of business, respectively. For the risk vector generated by the multiple lines of business, we suppose that the marginal distributions are fixed, but the dependence structure between these risks is unknown. Due to the unknown dependence structure, the optimal strategy is investigated for the worst-case scenario. We consider two types of risk measures: Value-at-Risk (VaR) and Range-Value-at-Risk (RVaR) including Expected Shortfall (ES) as a special case, and general premium principles satisfying certain conditions. To be more practical, the minimization of the total risk is conducted under some budget constraint. For the VaR-based model with only two risks, it turns out that the limited stop-loss reinsurance treaty is optimal for each line of business. For the model with more than two risks, we obtain two types of optimal reinsurance strategies if the marginals have convex or concave distributions on their tail parts by constraining the ceded loss functions to be convex or concave. Moreover, as a special case, the optimal quota-share reinsurance with dependence uncertainty has been studied. Finally, after applying our findings to two risks, some studies have been implemented to obtain both the analytical and numerical optimal reinsurance policies.

Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game

Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game

Optimal dividend and risk control strategies for an insurer when there are multiple reinsurers with different risk attitudes

Suppose that insurer can control dividend, refinancing and reinsurance strategies dynamically. Different from the past, there are multiple reinsurers rather than sole reinsurer in the market. The insurer aim at finding the optimal strategies for maximizing the company’s value. It illustrates that refinancing can be considered iff the company has strong profitability; It should reduce reinsurance purchase when the surplus increases. The amount of risk ceded to the reinsurer depends on its risk attitude. The optimal dividend policy is of barrier type when the dividend rate is unbounded and is of threshold type when the dividend rate is bounded.

Optimal investment and reinsurance strategies for an insurer with regime-switching

Optimal investment and reinsurance strategies for an insurer with regime-switching

The optimal reinsurance strategy with price-competition between two reinsurers

We study optimal reinsurance for an insurer and two reinsurers in the market through stochastic game theory. The relationship between the insurer and reinsurers is described by a Stackelberg model, where reinsurers, as market leaders, set prices for reinsurance treaties, and the insurer, as a price taker, determines reinsurance demand. Furthermore, we employ a Nash game to model the price competition between the two reinsurers who adopt different premium principles: the variance premium principle and the expected value premium principle. Both the insurer and reinsurers aim to maximize their respective mean-variance cost functions, leading to a time inconsistency control problem. This issue is resolved using a corresponding extended Hamilton-Jacobi-Bellman equation in the game-theoretic framework. We find that the insurer will adopt propositional and excess-of-loss reinsurance strategies with two reinsurers, respectively. Moreover, under an exponential claim size distribution, there exists a unique equilibrium reinsurance premium strategy. Our numerical analysis illuminates the effects of claim size, risk aversion, and the interest rates of the insurer and reinsurers on the equilibrium reinsurance and premium strategies, enhancing the understanding of competition in the reinsurance market.

The impact of market competitors on the demand for reinsurance

PurposeAccording to the market competition theory, a firm’s decision-making is influenced by the behaviors or strategies of its competitors. The repercussions of competition include market-stealing and spillover effects. Relatively few studies in the reinsurance literature discuss the effect of competitors on an insurer’s decision-making. This study aims to fill a gap in the reinsurance literature by comparing insurers' reinsurance demand to their competitors' reinsurance purchases.Design/methodology/approachThis study uses unbalanced panel data for the US property-liability insurance industry from 2006 to 2017 to determine the impact of competitors' reinsurance purchases on insurers' reinsurance demand. This study employs the Mixed Effect Model and the Quantile Regression to test the proposed hypotheses.FindingsThe evidence suggests that the affiliated reinsurance purchases of competitors have a positive and substantial effect on the affiliated reinsurance demand of insurers, crediting mimicking the reinsurance strategy. Interestingly, the market-stealing effect is supported while the non-affiliated reinsurance metric is used. Remarkably, given insurers with low non-affiliated reinsurance purchases, the finding sustains the mimicking reinsurance strategy. Nevertheless, the market-stealing effect remains a concern for insurers with a high non-affiliated reinsurance purchase.Originality/valueThe new findings concerning competitor effects analysis fill a void in the reinsurance literature. Risk diversification, capital substitution, and real services demand may play a crucial role in determining the market-stealing effect, leading to a decrease in market share. Insurers can mitigate the market-stealing effect of competitors by accessing expertise and capital substitution through non-affiliated reinsurance purchases.

Stackelberg differential reinsurance and investment game for a dependent risk model with Ornstein–Uhlenbeck process

This paper considers a reinsurance and investment problem under the Stackelberg differential game. It assumes that the insurer can purchase reinsurance and the claim businesses between the insurer and the reinsurer are correlated through common shock dependence, and both of them are allowed to invest in a common risky asset whose price follows an Ornstein–Uhlenbeck process. By the stochastic control theory, explicit expressions of the optimal controls and the value functions are obtained for both of the insurer and reinsurer. We show that the optimal reinsurance strategy is a constant, which is independent of the time and risk-free interest rate. We also show that compared with the independent model, the insurer will purchase less reinsurance and the reinsurer will increase the premium price under the dependent risk model.

Ruin probability for heavy-tailed and dependent losses under reinsurance strategies

The frequency and severity of extreme events have increased in recent years in many areas. In the context of risk management for insurance companies, reinsurance provides a safe solution as it offers coverage for large claims. This paper investigates the impact of dependent extreme losses on ruin probabilities under four types of reinsurance: excess of loss, quota share, largest claims, and ecomor. To achieve this, we use the dynamic GARCH-EVT-Copula combined model to fit the specific features of claim data and provide more accurate estimates compared to classical models. We derive the surplus processes and asymptotic ruin probabilities under the Cramér–Lundberg risk process. Using a numerical example with real-life data, we illustrate the effects of dependence and the behavior of reinsurance strategies for both insurers and reinsurers. This comparison includes risk premiums, surplus processes, risk measures, and ruin probabilities. The findings show that the GARCH-EVT-Copula model mitigates the over- and under-estimation of risk associated with extremes and lowers the ruin probability for heavy-tailed distributions.

Equilibrium Reinsurance Strategy and Mean Residual Life Function

Equilibrium Reinsurance Strategy and Mean Residual Life Function

The Time-Consistent Optimal Reinsurance Strategy of Insurance Group under the CEV Model

The article introduces proportional reinsurance contracts under the mean-variance criterion, studying the time-consistence investment portfolio problem considering the interests of both insurance companies and reinsurance companies. The insurance claims process follows a jump-diffusion model, assuming that the risk asset prices of insurance companies and reinsurance companies follow CEV models different from each other. In the framework of game theory, the time-consistent equilibrium reinsurance strategy is obtained by solving the extended HJB equation analytically. Finally, numerical examples are used to illustrate the impact of model parameters on equilibrium strategies and provide economic explanations. The results indicate that the decision weights of insurance companies and reinsurance companies do have a significant impact on both the reinsurance ratio and the equilibrium reinsurance strategy.

Optimal dividend and proportional reinsurance strategy for the risk model with common shock dependence

. This article focuses on the classic optimal dividend and reinsurance problems. Different from the existing literature, it assumes that the insurance company has two lines of business with a common shock dependence. It can purchase proportional reinsurance to reduce business risk and pay dividends to stay competitive. The goal is to find out the optimal dividend and reinsurance strategies for maximizing the company’s value. Under the diffusion approximation model, we decomposed the problem into several situations and gave the corresponding solutions by using the stochastic control method. Some numerical examples and economic explanations are presented to illustrate the results.

Equilibrium investment–reinsurance strategy under information asymmetry and random horizon

This paper investigates an investment–reinsurance problem incorporating information asymmetry and random horizon. At the beginning of the transaction, the insurer owns some inside information related to the risky asset price and the insurance claims. Simultaneously, the return rate and the driving noise for the risky asset process cannot be observed directly. Moreover, the trading horizon is random due to some exogenous factors. Under the dynamic mean–variance criterion, the equilibrium feedback strategy and the associated equilibrium value function are derived in closed form by solving the extended Hamilton–Jacobi–Bellman (HJB) equations. Several special cases are further discussed. Finally, numerical simulations are conducted to analyze the influences of some important parameters on the equilibrium strategy and the efficient frontier.

Optimal mean-variance investment and reinsurance strategies with a general Lévy process risk model

This paper is concerned with the optimal time-consistent investment and reinsurance strategies for mean-variance insurers with a general Lévy Process model. Expressly, the insurers are allowed to purchase proportional reinsurance and invest in a financial market, where the surplus of the insurers is assumed to follow a Cramér–Lundberg model and the financial market consists of one risk-free asset and one risky asset whose price process is driven by a general Lévy process. Through the verification theorem, the closed-form expressions of the optimal strategies under the mean-variance criterion are derived by a complex partial integral differential Hamilton–Jacobi–Bellman equations. Finally, numerical simulations are provided to verify the effectiveness of the proposed optimal strategies and some economic interpretations are drawn.

Non-zero-sum reinsurance and investment game under thinning dependence structure: mean–variance premium principle

This paper considers a non-zero-sum stochastic differential reinsurance and investment game between two competitive insurers under the expected exponential utility. It is assumed that the surplus process of each insurer is characterized by a compound Poisson model and their claim businesses are correlated through thinning dependence structure. Each insurer can purchase proportional reinsurance and is allowed to invest in a risk-free asset and a risky asset. The insurers compete with each other and are concerned with the relative performance. By using the stochastic control technique, not only the existence and uniqueness of the optimal strategies are proved, but also the specific analyses for the constraint reinsurance strategies are provided. We find that (i) the thinning dependence structure has significant impact on optimal reinsurance strategies for both insurers and can help them reduce risks; (ii) the behavior of non-zero-sum game will reduce the proportion of purchasing reinsurance for each insurer.

Expected power utility maximization with delay for insurers under the 4/2 stochastic volatility model

In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer with delay under the $ 4/2 $ stochastic volatility model. Indeed, the objective of the insurer is to maximize the expected power utility of the terminal wealth and the average wealth on finite time horizon. The other objective is to maximize the growth rate of expected power utility per unit time on infinite time horizon. The wealth of the insurer is described by an approximation of the classical Cramér–Lundberg process. Then, these problems can be formulated as stochastic control problems with delay. A pair of forward-backward stochastic differential equations that are derived via the stochastic maximum principle has an explicit solution obtained by solving a Riccati differential equation. So, the optimal strategy of the finite time horizon problem can be constructed explicitly. And, by investigating asymptotics of the Riccati equation, the infinite time horizon problem can be solved explicitly. Finally, we present some numerical results to illustrate our model, optimal strategies and sensitivities of some parameters.

Equilibrium per-loss reinsurance strategy with delay factors and ambiguity aversion under the cooperation framework

Equilibrium per-loss reinsurance strategy with delay factors and ambiguity aversion under the cooperation framework

Investigations to the optimal derivative-based investment and proportional reinsurance strategies

Investigations to the optimal derivative-based investment and proportional reinsurance strategies

Worst-Case Reinsurance Strategy with Likelihood Ratio Uncertainty

Worst-Case Reinsurance Strategy with Likelihood Ratio Uncertainty

Optimal reinsurance-investment problem with default risk for an insurer under the constant elasticity of variance model

Abstract Accepted by: Giorgio Consigli In this paper we study the optimal reinsurance-investment problem for an insurer with constant absolute risk aversion (CARA) utility. Because the insurer needs to avoid large claims and make profits in the actual operation process, he/she is allowed to buy proportional reinsurance and invest in a risk-free bond, a stock and a default bond. Moreover, the price process of the stock follows the constant elasticity of variance (CEV) model and the correlation between the risk process and the stock’s price is considered. For the objective of expected utility maximization, we establish the Hamilton–Jacobi–Bellman equation and derive the optimal reinsurance-investment strategy explicitly for the pre-default case and the post-default case via the dynamic programming. Finally, numerical examples and sensitivity analyses are provided to illustrate the effects of model parameters on the optimal strategy. We find that (i) the default risk has no impact on the optimal strategy of the stock and the parameters of the stock’s price have no impact on the optimal money amount invested in the defaultable bond. (ii) The optimal reinsurance strategy depends on the volatility of the stock’s price under the CEV model. (iii) The correlation between risk model and the stock’s price does have effects on the insurer’s optimal reinsurance-investment strategy. These findings may provide guidance to the management of insurers in practice.