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We show that the problem of existence of equilibrium in Kyle's continuoustime insider trading model can be tackled by considering a forward-backwardsystem coupled via an optimal transport type constraint at maturity. Theforward component is a stochastic differential equation representing anendogenously determined state variable and the backward component is aquasilinear parabolic equation representing the pricing function. By obtaininga stochastic representation for the solution of such a system, we show thewell-posedness of solutions and study the properties of the equilibriumobtained for small enough risk aversion parameter. In our model, the insiderhas exponential type utility and the belief of the market maker on thedistribution of the price at final time can be non-Gaussian.

Kyle-Back Models with risk aversion and non-Gaussian Beliefs