为了助力传统产业转型升级，探索统计理论与应用融合发展，基地重大项目“数字时代风险管理与精算模型研究”应用大数据和人工智能方法对风险管理与保险精算领域的若干重要问题进行了研究，包括宏观经济金融风险管理、农业风险管理、保险产品与服务等领域。以下是项目组在金融保险中的最优决策问题领域的近期研究成果：

1. Guan G, Liang Z, Xia J. Equilibrium portfolio selection for smooth ambiguity preferences[J]. Mathematics of Operations Research, 2024. Online.

2. Guan G, Liang Z, Ma X. Optimal annuitization and asset allocation under linear habit formation[J]. Insurance: Mathematics and Economics, 2024, 114: 176-191.

3. Guan G, Liang Z, Song Y. A Stackelberg reinsurance-investment game under α-maxmin mean-variance criterion and stochastic volatility[J]. Scandinavian Actuarial Journal, 2024, (1): 28-63.

4. Guan G, He L, Liang Z, et al. Robust dividend, financing, and reinsurance strategies under model uncertainty with proportional transaction costs[J]. North American Actuarial Journal, 2024, 28(2): 261-284.

5. Liu B, Zhang L, Zhou M. Portfolio selections for insurers with ambiguity aversion: minimizing the probability of ruin[J]. Applied Economics, 2024, 56(12): 1423-1439. 

论文题目与摘要

1.Guan G, Liang Z, Xia J. Equilibrium portfolio selection for smooth ambiguity preferences[J]. Mathematics of Operations Research, 2024. Online.

Abstract: This paper investigates the equilibrium portfolio selection for smooth ambiguity preferences in a continuous-time market. The investor is uncertain about the risky asset’s drift term and updates the subjective belief according to the Bayesian rule. A verification theorem is established, and an equilibrium strategy can be decomposed into a myopic demand and two hedging demands. When the prior is Gaussian, we provide an equilibrium solution in closed form. Moreover, a puzzle in the numerical results is interpreted via an alternative representation of the smooth ambiguity preferences.

Keywords: Bayesian learning ；Smooth ambiguity；Time inconsistency；Equilibrium strategy

2.Guan G, Liang Z, Ma X. Optimal annuitization and asset allocation under linear habit formation[J]. Insurance: Mathematics and Economics, 2024, 114: 176-191.

Abstract: This paper studies the optimal consumption-investment-annuitization problem for a retiree with linear consumption habits. We explore the effect of consumption habits on the decision to annuitize when annuities are purchased as a lump sum. The problem is formulated as a combined stopping-control problem. We derive optimal annuitization time, investment, and consumption strategies by a generalized dual method and habit reduction method. We investigate the influence of various factors on the annuitization time and derive optimal annuitization time, which is a barrier strategy. The numerical simulations reveal several interesting results. Our results demonstrate that risk aversion, subjective hazard rate, and consumption habits all play a role in shaping annuitization decisions. Furthermore, we offer a new explanation for the rarity of voluntary annuitization among retirees.

Key words:   Linear habit formation; Stopping-control problem; Annuitization; Dual methods;  Variational inequalities

3.Guan G, Liang Z, Song Y. A Stackelberg reinsurance-investment game under α-maxmin mean-variance criterion and stochastic volatility[J]. Scandinavian Actuarial Journal, 2024, (1): 28-63.

Abstract: This paper investigates a Stackelberg game between an insurer and a reinsurer under the α-maxmin mean-variance criterion. The insurer can purchase per-loss reinsurance from the reinsurer. With the insurer’s feedback reinsurance strategy, the reinsurer optimizes the reinsurance premium in the Stackelberg game. The financial market consists of cash and stock with Heston’s stochastic volatility. Both the insurer and reinsurer maximize their respective α-maxmin mean-variance preferences in the market. The criterion is time-inconsistent and we derive the equilibrium strategies by the extended Hamilton-Jacobi-Bellman equations. Similar to the nonrobust case in [Li, D. & Young, V. R. (2022). Stackelberg differential game for reinsurance: mean-variance framework and random horizon. Insurance: Mathematics and Economics 102, 42–55.], excess-of-loss reinsurance is the optimal form of reinsurance strategy for the insurer. The equilibrium investment strategy is determined by a system of Riccati differential equations. Besides, the equations determining the equilibrium reinsurance strategy and reinsurance premium rate are given semi-explicitly, which is simplified to an algebraic equation in a specific example. Numerical examples illustrate that the game between the insurer and reinsurer makes the insurance more radical when the agents become more ambiguity averse or risk averse. Furthermore, the level of ambiguity, ambiguity attitude, and risk attitude of the insurer (reinsurer) have similar effects on the equilibrium reinsurance strategy, reinsurance premium, and investment strategy. 

Keywords:    Stackelberg game; Reinsurance; investment; Stochastic volatility; Model uncertainty; α-maxmin mean-variance

4.Guan G, He L, Liang Z, et al. Robust Dividend, Financing, and Reinsurance Strategies Under Model Uncertainty with Proportional Transaction Costs[J]. North American Actuarial Journal, 2024, 28(2): 261-284.

Abstract: This article studies the robust dividend, financing, and reinsurance strategies for an ambiguity aversion insurer (AAI) under model uncertainty. The AAI controls its liquid reserves by purchasing proportional reinsurance, paying dividends, and issuing new equity. We consider model uncertainty and suppose that the AAI is ambiguous about the liquid reserves process, which is described by a class of equivalent probability measures. The objective of the AAI is to maximize the expected present value of the dividend payouts minus the discounted costs of issuing new equity before bankruptcy under the worst-case scenario. A detailed proof of the verification theorem is shown for the robust singular-regular problem. We obtain the explicit solutions of the robust strategies, which are classified into three cases. Numerical results are also presented to show the impacts of the ambiguity aversion coefficient, and the transaction cost factor.

Keywords:  Dividend; Financing; Reinsurance; Ambiguity aversion

5.Liu B, Zhang L, Zhou M. Portfolio selections for insurers with ambiguity aversion: minimizing the probability of ruin[J]. Applied Economics, 2024, 56(12): 1423-1439. 

Abstract: In this paper, we investigate the impacts of model misspecification on the insurer’s investment behaviours. Model misspecification comes from either the financial market or insurance business due to economic fluctuation. From the risk control point of view, we assume that an insurer has ambiguity aversion and we study the robust optimal investment strategy for the insurer under several settings. As a benchmark, we firstly obtain the optimal investment strategy for the insurer without considering model misspecification. Then, by assuming that model misspecification only exists in the financial market, we obtained the robust optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation under the objective of minimizing the probability of ruin. The results tells us the insurer’s ambiguity aversion leads to a more conservative investment behaviour. At last, we incorporate the model misspecification for both financial market and insurance business in a general framework. The robust optimal investment is also obtained and we find that the investment is enlarged due to the insurer’s ambiguity aversion on the insurance business because of the motivation of ambiguity hedging. The numerical examples display that different ambiguity aversion level on the financial market and insurance business have different impacts on the robust investment strategy. 

Keywords: HJB equation; Model misspecification; Ambiguity aversion; Probability of ruin; Portfolio selection