Current Research Interests
Current Research Interests
- Financial and Actuarial Mathematics
- Stochastic Control and Optimal Stopping
Publications
Publications
Ferrari, G., Schuhmann, P., and Zhu, S. (2022). Optimal Dividends under Markov-modulated Bankruptcy Level. Insurance: Mathematics and Economics, 106, 146-172.
Ferrari, G., Schuhmann, P., and Zhu, S. (2022). Optimal Dividends under Markov-modulated Bankruptcy Level. Insurance: Mathematics and Economics, 106, 146-172.
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.
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.
Preprints
Preprints
Chen, A., Ferrari, G., and Zhu, S. (2023). Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning. https://arxiv.org/abs/2312.02943.
Chen, A., Ferrari, G., and Zhu, S. (2023). Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning. https://arxiv.org/abs/2312.02943.
This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent's option to choose when to acquire life insurance for bequest purposes. We examine two scenarios: one with a fixed bequest amount and another with a controlled bequest amount. Applying duality theory and addressing free-boundary problems, we analytically solve both cases, and provide explicit expressions for value functions and optimal strategies in both cases.
This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent's option to choose when to acquire life insurance for bequest purposes. We examine two scenarios: one with a fixed bequest amount and another with a controlled bequest amount. Applying duality theory and addressing free-boundary problems, we analytically solve both cases, and provide explicit expressions for value functions and optimal strategies in both cases.
Ferrari, G., and Zhu, S. (2023). Optimal Retirement Choice under Age-dependent Force of Mortality. https://arxiv.org/abs/2311.12169
Ferrari, G., and Zhu, S. (2023). Optimal Retirement Choice under Age-dependent Force of Mortality. https://arxiv.org/abs/2311.12169
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.
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.
Ferrari, G., and Zhu, S. (2022). On a Merton Problem with Irreversible Healthcare Investment. https://arxiv.org/abs/2212.05317.
Ferrari, G., and Zhu, S. (2022). On a Merton Problem with Irreversible Healthcare Investment. https://arxiv.org/abs/2212.05317.
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.
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.
Work in Progress
Work in Progress
- "Optimal Stopping under Smooth Ambiguity Model" (with Yu-Jui Huang)