<p>We study a continuous-time economy where throughout time, insiders receive private signals regarding the risky assets’ terminal payoff. We prove existence of a partial communication equilibrium where at each private signal time, the public receives a signal of the same form as the associated insider, but of lower quality. This causes a jump in both the public information flow and the equilibrium asset price. The resultant markets, while complete between each jump time, are incomplete over each jump. After establishing equilibrium for a finite number of private signal times, we consider the limit as the private signals become more and more frequent. Under appropriate scaling, we prove convergence of the public filtration to the natural filtration generated by both the fundamental factor process <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_565_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>X</mi> </math></EquationSource> <EquationSource Format="TEX">$X$</EquationSource> </InlineEquation> and a continuous time process <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_565_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>J</mi> </math></EquationSource> <EquationSource Format="TEX">$J$</EquationSource> </InlineEquation> taking the form <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_565_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>J</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>Y</mi> <mi>t</mi> </msub> </math></EquationSource> <EquationSource Format="TEX">$J_{t} = X_{1} + Y_{t}$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_565_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mn>1</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$X_{1}$</EquationSource> </InlineEquation> is the terminal payoff and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_565_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>Y</mi> </math></EquationSource> <EquationSource Format="TEX">$Y$</EquationSource> </InlineEquation> an independent Gaussian process. This coincides with the filtration considered in Corcuera et al. (Finance Stoch. 8:437–450, <CitationRef CitationID="CR15">2004</CitationRef>). However, while the filtration there was exogenously assumed to be that of an insider who observes a private signal flow, here it arises endogenously as the public filtration when there are a large number of insiders receiving signals throughout time.</p>

Equilibrium with heterogeneous information flows

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发表日期：

2025年5月20日

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Scott Robertson

摘要

We study a continuous-time economy where throughout time, insiders receive private signals regarding the risky assets’ terminal payoff. We prove existence of a partial communication equilibrium where at each private signal time, the public receives a signal of the same form as the associated insider, but of lower quality. This causes a jump in both the public information flow and the equilibrium asset price. The resultant markets, while complete between each jump time, are incomplete over each jump. After establishing equilibrium for a finite number of private signal times, we consider the limit as the private signals become more and more frequent. Under appropriate scaling, we prove convergence of the public filtration to the natural filtration generated by both the fundamental factor process $X$ $X$ and a continuous time process $J$ $J$ taking the form $J_{t} = X_{1} + Y_{t}$ $J_{t} = X_{1} + Y_{t}$ , where $X_{1}$ $X_{1}$ is the terminal payoff and $Y$ $Y$ an independent Gaussian process. This coincides with the filtration considered in Corcuera et al. (Finance Stoch. 8:437–450, 2004). However, while the filtration there was exogenously assumed to be that of an insider who observes a private signal flow, here it arises endogenously as the public filtration when there are a large number of insiders receiving signals throughout time.