강연 / 세미나
PDE and Applied Analysis Seminar
분야Field | |||
---|---|---|---|
날짜Date | 2023-06-16 ~ 2023-06-16 | 시간Time | 11:00 ~ 12:00 |
장소Place | online | 초청자Host | |
연사Speaker | Tak Kwong Wong | 소속Affiliation | 홍콩대학교(University of Hong Kong) |
TOPIC | PDE and Applied Analysis Seminar | ||
소개 및 안내사항Content | Title: On the Well-posedness of Classical Solutions to Hamilton-Jacobi-Bellman Equation Arising from the Optimal Savings and the Value of Population Problem under a Stochastic Environment
Abstract: In the work of Arrow et al. (2007, Proc. Natl. Acad. Sci. U.S.A.), they studied a macroeconomic growth model so that the population dynamic was involved in both the total utility (objective function) of the whole population and in the capital investment process. In essence, they assumed the deterministic evolution for both dynamics, such that the labour force of the population is also incurred through the Cobb-Douglas production function. In this talk, we will first introduce an extension of their problem, particularly over a finite time horizon, in which we also allow more realistic and generic population growth and incorporate a stochastic environment for both the demography and capital investment. For the corresponding Hamilton-Jacobi-Bellman equation, we show the existence and uniqueness of classical solutions by using a hybrid approach that combines techniques in both partial differential equations and stochastic analysis. We believe that the methodology developed in this work can also apply to various sophisticated models arising from economic growth theory and mathematical finance. This work is supported by the Hong Kong General Research Fund “Controlling the Growth of Classical Solutions of a Class of Parabolic Differential Equations with Singular Coefficients: Resolutions for Some Lasting Problems from Economics” with project number 17302521. Reference: Arrow, K., Bensoussan, A., Feng, Q., and Sethi, S.P. (2007). Optimal savings and the value of population, Proceedings of the National Academy of Sciences, 47: 18421-6. |
학회명Field | PDE and Applied Analysis Seminar | ||
---|---|---|---|
날짜Date | 2023-06-16 ~ 2023-06-16 | 시간Time | 11:00 ~ 12:00 |
장소Place | online | 초청자Host | |
소개 및 안내사항Content | Title: On the Well-posedness of Classical Solutions to Hamilton-Jacobi-Bellman Equation Arising from the Optimal Savings and the Value of Population Problem under a Stochastic Environment
Abstract: In the work of Arrow et al. (2007, Proc. Natl. Acad. Sci. U.S.A.), they studied a macroeconomic growth model so that the population dynamic was involved in both the total utility (objective function) of the whole population and in the capital investment process. In essence, they assumed the deterministic evolution for both dynamics, such that the labour force of the population is also incurred through the Cobb-Douglas production function. In this talk, we will first introduce an extension of their problem, particularly over a finite time horizon, in which we also allow more realistic and generic population growth and incorporate a stochastic environment for both the demography and capital investment. For the corresponding Hamilton-Jacobi-Bellman equation, we show the existence and uniqueness of classical solutions by using a hybrid approach that combines techniques in both partial differential equations and stochastic analysis. We believe that the methodology developed in this work can also apply to various sophisticated models arising from economic growth theory and mathematical finance. This work is supported by the Hong Kong General Research Fund “Controlling the Growth of Classical Solutions of a Class of Parabolic Differential Equations with Singular Coefficients: Resolutions for Some Lasting Problems from Economics” with project number 17302521. Reference: Arrow, K., Bensoussan, A., Feng, Q., and Sethi, S.P. (2007). Optimal savings and the value of population, Proceedings of the National Academy of Sciences, 47: 18421-6. |
성명Field | PDE and Applied Analysis Seminar | ||
---|---|---|---|
날짜Date | 2023-06-16 ~ 2023-06-16 | 시간Time | 11:00 ~ 12:00 |
소속Affiliation | 홍콩대학교(University of Hong Kong) | 초청자Host | |
소개 및 안내사항Content | Title: On the Well-posedness of Classical Solutions to Hamilton-Jacobi-Bellman Equation Arising from the Optimal Savings and the Value of Population Problem under a Stochastic Environment
Abstract: In the work of Arrow et al. (2007, Proc. Natl. Acad. Sci. U.S.A.), they studied a macroeconomic growth model so that the population dynamic was involved in both the total utility (objective function) of the whole population and in the capital investment process. In essence, they assumed the deterministic evolution for both dynamics, such that the labour force of the population is also incurred through the Cobb-Douglas production function. In this talk, we will first introduce an extension of their problem, particularly over a finite time horizon, in which we also allow more realistic and generic population growth and incorporate a stochastic environment for both the demography and capital investment. For the corresponding Hamilton-Jacobi-Bellman equation, we show the existence and uniqueness of classical solutions by using a hybrid approach that combines techniques in both partial differential equations and stochastic analysis. We believe that the methodology developed in this work can also apply to various sophisticated models arising from economic growth theory and mathematical finance. This work is supported by the Hong Kong General Research Fund “Controlling the Growth of Classical Solutions of a Class of Parabolic Differential Equations with Singular Coefficients: Resolutions for Some Lasting Problems from Economics” with project number 17302521. Reference: Arrow, K., Bensoussan, A., Feng, Q., and Sethi, S.P. (2007). Optimal savings and the value of population, Proceedings of the National Academy of Sciences, 47: 18421-6. |
성명Field | PDE and Applied Analysis Seminar | ||
---|---|---|---|
날짜Date | 2023-06-16 ~ 2023-06-16 | 시간Time | 11:00 ~ 12:00 |
호실Host | 인원수Affiliation | Tak Kwong Wong | |
사용목적Affiliation | 신청방식Host | 홍콩대학교(University of Hong Kong) | |
소개 및 안내사항Content | Title: On the Well-posedness of Classical Solutions to Hamilton-Jacobi-Bellman Equation Arising from the Optimal Savings and the Value of Population Problem under a Stochastic Environment
Abstract: In the work of Arrow et al. (2007, Proc. Natl. Acad. Sci. U.S.A.), they studied a macroeconomic growth model so that the population dynamic was involved in both the total utility (objective function) of the whole population and in the capital investment process. In essence, they assumed the deterministic evolution for both dynamics, such that the labour force of the population is also incurred through the Cobb-Douglas production function. In this talk, we will first introduce an extension of their problem, particularly over a finite time horizon, in which we also allow more realistic and generic population growth and incorporate a stochastic environment for both the demography and capital investment. For the corresponding Hamilton-Jacobi-Bellman equation, we show the existence and uniqueness of classical solutions by using a hybrid approach that combines techniques in both partial differential equations and stochastic analysis. We believe that the methodology developed in this work can also apply to various sophisticated models arising from economic growth theory and mathematical finance. This work is supported by the Hong Kong General Research Fund “Controlling the Growth of Classical Solutions of a Class of Parabolic Differential Equations with Singular Coefficients: Resolutions for Some Lasting Problems from Economics” with project number 17302521. Reference: Arrow, K., Bensoussan, A., Feng, Q., and Sethi, S.P. (2007). Optimal savings and the value of population, Proceedings of the National Academy of Sciences, 47: 18421-6. |