Existence of an equilibrium with limited stock market participation and power utilities
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913247516426240 |
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| author | Guasoni, Paolo Larsen, Kasper Leoni, Giovanni |
| author_facet | Guasoni, Paolo Larsen, Kasper Leoni, Giovanni |
| contents | For constants $γ\in (0,1)$ and $A\in (1,\infty)$, we prove existence and uniqueness of a solution to the singular and path-dependent Riccati-type ODE \begin{align*} \begin{cases} h'(y) = \frac{1+γ}{y}\big( γ- h(y)\big)+h(y)\frac{γ+ \big((A-γ)e^{\int_y^1 \frac{1-h(q)}{1-q}dq}-A\big)h(y)}{1-y},\quad y\in(0,1), h(0) = γ, \quad h(1) = 1. \end{cases} \end{align*} As an application, we use the ODE solution to prove existence of a Radner equilibrium with homogenous power-utility investors in the limited participation model from Basak and Cuoco (1998). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of an equilibrium with limited stock market participation and power utilities Guasoni, Paolo Larsen, Kasper Leoni, Giovanni Mathematical Finance Analysis of PDEs For constants $γ\in (0,1)$ and $A\in (1,\infty)$, we prove existence and uniqueness of a solution to the singular and path-dependent Riccati-type ODE \begin{align*} \begin{cases} h'(y) = \frac{1+γ}{y}\big( γ- h(y)\big)+h(y)\frac{γ+ \big((A-γ)e^{\int_y^1 \frac{1-h(q)}{1-q}dq}-A\big)h(y)}{1-y},\quad y\in(0,1), h(0) = γ, \quad h(1) = 1. \end{cases} \end{align*} As an application, we use the ODE solution to prove existence of a Radner equilibrium with homogenous power-utility investors in the limited participation model from Basak and Cuoco (1998). |
| title | Existence of an equilibrium with limited stock market participation and power utilities |
| topic | Mathematical Finance Analysis of PDEs |
| url | https://arxiv.org/abs/2402.07185 |