We show the existence of a continuous-time Nash equilibrium in a financial market with risk averse market makers and an informed trader with a private information. The unwillingness of market makers to bear risk causes the informed trader to absorb large shocks in their inventories. The informed trader's optimal strategy is to drive the market price to its fundamental value while participating in the risk sharing with the market makers. The optimal strategies of the agents turn out to be solutions of a forward-backward system of partial and stochastic differential equations. In particular, the price set by the market makers is the solution to a non-standard `quadratic' backward stochastic differential equation  .
This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward-backward system of partial and stochastic differential equations. In particular, the price set by the market makers solves a nonstandard "quadratic" backward stochastic differential equation . The main result of the paper is the existence of a Markovian solution to this forward-backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models .
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We show the existence of a
This paper develops a new methodology for studying
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risk averse market makers and an informed trader with a private information. The unwillingness of market makers to bear risk causes the informed trader to absorb large shocks in their inventories. The informed trader's optimal strategy is to drive the market price to its fundamental value while participating in the risk sharing with the market makers. The
asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the
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turn out to be
are
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is the solution to a non-standard `quadratic'
solves a nonstandard "quadratic"
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. The main result of the paper is the existence of a Markovian solution to this forward-backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models