Optimal Time-consistent Investment and Reinsurance Strategy for Mean-variance Insurers Under the Inside Information

In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.

Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework

This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.

Time-consistent investment and reinsurance strategies for insurers under multi-period mean-variance formulation with generalized correlated returns

The existing literature on investment and reinsurance is limited to the study of continuous-time problems,while discrete-time problems are always ignored by re-searchers.In this study,we first discuss a multi-period investment and reinsurance opti-mization problem under the classical mean-variance framework.When the asset returns with a serially correlated structure,the time-consistent investment and reinsurance strategies are acquired via backward induction.In addition,we propose an alternative time-consistent mean-variance optimization model that contrasts with the classical mean-variance model,and the corresponding optimal strategy and value function are also derived.We find that the investment and reinsurance strategies are both independent of the current wealth for the above two optimization problems,which coincides with the conclusion presented in the continuous-time problems.Most importantly,the above in-vestment strategies with serially correlated structures are both conditional mean-based strategies,rather than unconditional ones.Finally,we compare the investment and rein-surance strategies suggested above based on the simulation approach,to shed light on which investment-reinsurance strategies are more suitable for insurers.

Time-Consistent Investment Strategy for DC Pension Plan with Stochastic Salary Under CEV Model

This paper aims to derive the time-consistent investment strategy for the defined contribution(DC) pension plan under the mean-variance criterion.The financial market consists of a risk-free asset and a risky asset of which price process satisfies the constant elasticity of variance(CEV) model.Compared with the geometric Brownian motion model,the CEV model has the ability of capturing the implied volatility skew and explaining the volatility smile.The authors assume that the contribution to the pension fund is a constant proportion of the pension member's salary.Meanwhile,the salary is stochastic and its volatility arises from the price process of the risky asset,which makes the proposed model different from most of existing researches and more realistic.In the proposed model,the optimization problem can be decomposed into two sub-problems:Before and after retirement cases.By applying a game theoretic framework and solving extended Hamilton-Jacobi-Bellman(HJB) systems,the authors derive the time-consistent strategies and the corresponding value functions explicitly.Finally,numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategies.