This paper investigates an optimal insurance contracting problem under preference robustness from the perspective of a potential policyholder. The preferences of this potential policyholder are modeled using a worst-case distortion risk measure, considering various ambiguity sets for the distortion function. Here, robustness is modeled for the distortion function itself, rather than for the probability distribution of the loss. The optimal indemnity function exhibits a layered structure. When the ambiguity set is constructed based on the assessments of continuous loss variables, the worst-case distortion function takes a piecewise form. Incorporating additional assessments of discrete loss variables further influences the left or right tail of the worst-case distortion function. If the concavity of the distortion function is common knowledge a priori, the worst-case distortion function is shown to be piecewise linear with at most three segments. A unified linear programming approach is developed to solve problems involving finitely supported loss variables. Numerical examples are provided to illustrate the practical implications of our findings.
This paper investigates how additional independent background risks (e.g. fluctuations in financial asset prices, human capital, etc.) affect higher-order stochastic dominance. We show that an appropriately chosen background risk can induce a ranking of prospects under higher-order stochastic dominance according to the magnitude of their higher-order central moments. In addition, we provide an equivalent representation of mean–variance–skewness preferences. This representation can be characterized by the four properties of certainty, downside risk monotonicity, additivity, and skewness-free continuity, and it further strengthens the connection between mean–variance–skewness preferences and third-order stochastic dominance.
This paper investigates a Stackelberg investment and reinsurance game with the ambiguous correlation between the financial and insurance markets. The ambiguous correlation is modeled by constructing a set of non-equivalent prior probability measures. The reinsurer acts as the leader charging reinsurance premiums, while the insurer acts as the follower participating in proportional reinsurance. Both the reinsurer and the insurer invest in the financial market with the aim to maximize the expected utility of their terminal wealth under the worst-case scenario. The Stackelberg equilibrium strategy is derived by solving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. Through theoretical analysis and numerical simulation, the influence of ambiguity on the Stackelberg equilibrium strategy is analyzed. We find that both the insurer and reinsurer adopt more conservative strategies in the presence of market correlation ambiguity, with the insurer being more significantly affected by such ambiguity, while the reinsurer is less influenced. When both the insurer and the reinsurer maintain investment in the risky asset, the ambiguity faced by the insurer leads to higher reinsurance premiums, whereas the ambiguity faced by the reinsurer results in lower reinsurance premiums.
This paper develops an infinite-horizon, Lucas-type general equilibrium model of asset markets with a fuzzy decision-making investor. The model yields closed-form intuitive solutions for the equilibrium equity premium and risk-free rate. The solutions clearly separate the equity premium that investors demand for bearing measurable risk from the premium that arises from unmeasurable uncertainty. The magnitude of the premium for risk depends solely on risk aversion, whereas the premium for unmeasurable uncertainty reflects both investor sentiment and the degree of that uncertainty. Our results imply that a pessimistic outlook reduces the risk-free rate and increases the equity premium. Under reasonable parameterizations, the model generates the long-run first moments of the U.S. risk-free rate and equity premium with moderate risk aversion and without inflating the variance of equity returns. This work contributes to the asset-pricing literature by showing that fuzzy sets and membership functions provide a tractable and flexible framework for modeling approximate decision-making in asset markets.
This study proposes generalized homothetic robust Epstein-Zin (GHREZ) utility in which the coefficient of relative ambiguity aversion in homothetic the robust Epstein-Zin (HREZ) utility is generalized to a positive-definite “relative ambiguity aversion matrix.” We analyze a robust consumption–investment problem with the GHREZ utility under a quadratic security market model. We demonstrate that the volatility of the optimal robust portfolio can be expressed as a weighted average of the market price of risk and the “investor hedging value of intertemporal uncertainty.” We derive an approximate optimal robust portfolio and quantitatively analyze the relationship between the approximate optimal robust portfolios and relative ambiguity aversion matrices. Numerical analysis reveals that as deviations from the relative ambiguity aversion matrix under the HREZ utility increase, deviations from the approximate optimal asset allocation under the HREZ utility increase, and this sensitivity is significant. This finding suggests that the GHREZ utility is promising for solving the equity home bias puzzle.
