My research focuses on uncertainty and information in economic decision-making, with applications in insurance, health behavior, and finance.

I approach these questions using tools from risk management, actuarial and financial mathematics, and stochastic control and optimal stopping. 

【3】Chen, A., Ferrari, G., and Zhu, S. (2025). Striking the balance: life insurance timing and asset allocation in financial planning. Scandinavian Actuarial Journal, 1-40.

【2】Ferrari, G., Schuhmann, P., and Zhu, S. (2022). Optimal Dividends under Markov-modulated Bankruptcy Level. Insurance: Mathematics and Economics, 106, 146-172.

【1】Zhu, S., and Shi, J. (2022). Optimal Reinsurance and Investment Strategies under Mean-variance Criteria: Partial and Full Information. Journal of Systems Science and Complexity, 35(4), 1458-1479.

【6】Huang, Y. J., & Zhu, S. (2025). Mean-Variance Stackelberg Games with Asymmetric Information. https://arxiv.org/abs/2509.03669. Submitted.

We consider two investors who perform mean-variance portfolio selection with asymmetric information. Their portfolio selection is interconnected through relative performance concerns. We model this as Stackelberg competition. To prevent information leakage, the leader adopts a randomized strategy selected under an entropy-regularized mean-variance objective. In the idealized case of continuous sampling of the leader's trading actions, we derive a Stackelberg equilibrium where the follower's trading strategy depends linearly on the actual trading actions of the leader and the leader samples her trading actions from Gaussian distributions. 

【5】Chen, A., Hinken, M., & Zhu, S. (2025). Modeling of Biological and Subjective Age with Economic Applications. Available at SSRN 5382393. Submitted.

We propose a realistic yet parsimonious model of an individual's biological and subjective age. Moreover, our model explicitly incorporates the interaction between biological and subjective age, as documented in empirical studies (e.g., Stephan et al., 2015). It replicates key findings from the literature, such as the observation that biological age can differ up to 20 years from the chronological age (Bortz et al., 2023), or that people older than 40 believe to be 20% younger (Rubin and Berntsen, 2006). As an illustration, we apply the framework to a consumption and portfolio choice problem, where health-dependent utility functions are applied.

【4】Chen, A., and Zhu, S. (2025). Health-Wealth Complementarity and Ambiguity in Long-Term Care Insurance. Available at SSRN 5228627. Submitted.

We propose a parent-child framework where the parent’s utility depends on both wealth and health, and the child provides informal care. The sign of the cross-derivative U_{WH} indicates whether wealth and health are complements or substitutes, thereby determining the relationship between insurance and informal care, whether positive or negative. Under actuarially fair pricing, optimal coverage is partial when U_{WH} >0, but may exceed full formal-care costs when U_{WH} < 0. We then introduce smooth-ambiguity preferences over the uncertain efficiency of informal care. Ambiguity aversion raises (lowers) insurance demand when U_{WH} < 0 (U_{WH} > 0), because parents hedge against the prospect that informal care is less (more) effective than expected. 

【3】Chen, A., and Zhu, S. (2025). Optimal Consumption under Smooth Ambiguity. Available at SSRN 5131016. Submitted.

We study how individuals choose contingent consumption plans when the probabilities of future states are ambiguous and utility depends on the realized state. In both static one-period and intertemporal smooth-ambiguity settings, we show that ambiguity aversion shifts the decision-maker's subjective prior and alters the discount factor. We provide explicit sufficient conditions that characterize these shifts. Applying our framework to insurance economics, we illustrate how ambiguity aversion offers a compelling explanation for the "underinsurance puzzle" and the "annuity puzzle"-two longstanding challenges to standard expected-utility models.

【2】Ferrari, G., and Zhu, S. (2023). Optimal Retirement Choice under Age-dependent Force of Mortality. https://arxiv.org/abs/2311.12169. Submitted.

This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring three state variables: wealth, labor income, and force of mortality. Regularity of the optimal stopping value function is derived and the boundary is proved to be Lipschitz continuous, and it is characterized as the unique solution to a nonlinear integral equation, which we compute numerically. In the original coordinates, the agent thus retires whenever her wealth exceeds an age-, labor income- and mortality-dependent transformed version of the optimal stopping boundary. 

【1】Ferrari, G., and Zhu, S. (2022). On a Merton Problem with Irreversible Healthcare Investment. https://arxiv.org/abs/2212.05317. Revise & Resubmit with Finance and Stochastics. 

This paper proposes a tractable dynamic framework for the joint determination of optimal consumption, portfolio choice, and healthcare irreversible investment. The resulting optimization problem is formulated as a stochastic control-stopping problem with a random time-horizon and state-variables given by the agent’s wealth and health capital. We transform this problem into its dual version, which is now a two-dimensional optimal stopping problem with interconnected dynamics and finite time-horizon. In the original coordinates, the agent thus invests into healthcare whenever her wealth exceeds an age- and health-dependent transformed version of the optimal stopping boundary.