We investigate the problem of equilibrium price formation in an incomplete securities market. Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order-flows from its over-the-counter clients. We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the ] solution to a certain forward backward stochastic differential equation of conditional McKean-Vlasov type gives a good approximate of the equilibrium price which clears the market in the large population limit. In this work, we prove the existence of a unique market clearing equilibrium among the heterogeneous agents of finite population size. We show the strong convergence to the corresponding mean-field limit under suitable conditions. In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit ] .
We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work 15], we have shown that a certain price process, which is given by the solution to a forward backward stochastic differential equation of conditional McKean-Vlasov type , asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in 15]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size .
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investigate the problem of equilibrium price formation in an incomplete
study an equilibrium-based continuous asset pricing problem for the
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Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities exchange while facing the systemic and idiosyncratic noises as well as the stochastic order-flows from its over-the-counter clients. We have shown , in the accompanying paper (Fujii-Takahashi (2020)), that the
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, we have shown that a certain price process, which is given by the
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gives a good approximate of the equilibrium price which
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this work, we prove
the current work, under suitable conditions, we show
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unique market clearing equilibrium among the heterogeneous agents of finite population size. We show the
finite agent equilibrium and its
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under suitable conditions. In particular, we provide the stability relation between the market clearing price for the heterogeneous agents and that for the homogeneous mean-field limit
given in
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15
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. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size