Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909138084167680 |
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| author | Detemple, Jerome Robertson, Scott |
| author_facet | Detemple, Jerome Robertson, Scott |
| contents | We study a continuous time economy where agents have asymmetric information. The informed agent (``$I$''), at time zero, receives a private signal about the risky assets' terminal payoff $Ψ(X_T)$, while the uninformed agent (``$U$'') has no private signal. $Ψ$ is an arbitrary payoff function, and $X$ follows a time-homogeneous diffusion. Crucially, we allow $U$ to have von Neumann-Morgenstern preferences with a general utility function on $(0,\infty)$ satisfying the standard conditions. This extends previous constructions of equilibria with asymmetric information used when all agents have exponential utilities and enables us to study the impact of $U$'s initial share endowment on equilibrium. To allow for $U$ to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time $0$, $U$ receives a less-informative signal than $I$. In the single asset case, this signal is recoverable by viewing the equilibrium price process over an arbitrarily short period of time, and hence the PCE is a dynamic noisy rational expectations equilibrium. Lastly, when $U$ has power (constant relative risk aversion) utility, we identify the equilibrium price in the small and large risk aversion limits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_15573 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility Detemple, Jerome Robertson, Scott Mathematical Finance 91G30, 91B69 We study a continuous time economy where agents have asymmetric information. The informed agent (``$I$''), at time zero, receives a private signal about the risky assets' terminal payoff $Ψ(X_T)$, while the uninformed agent (``$U$'') has no private signal. $Ψ$ is an arbitrary payoff function, and $X$ follows a time-homogeneous diffusion. Crucially, we allow $U$ to have von Neumann-Morgenstern preferences with a general utility function on $(0,\infty)$ satisfying the standard conditions. This extends previous constructions of equilibria with asymmetric information used when all agents have exponential utilities and enables us to study the impact of $U$'s initial share endowment on equilibrium. To allow for $U$ to have general preferences, we introduce a new method to prove existence of a partial communication equilibrium (PCE), where at time $0$, $U$ receives a less-informative signal than $I$. In the single asset case, this signal is recoverable by viewing the equilibrium price process over an arbitrarily short period of time, and hence the PCE is a dynamic noisy rational expectations equilibrium. Lastly, when $U$ has power (constant relative risk aversion) utility, we identify the equilibrium price in the small and large risk aversion limits. |
| title | Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility |
| topic | Mathematical Finance 91G30, 91B69 |
| url | https://arxiv.org/abs/2211.15573 |