Actuarial Science and Financial Mathematics seminar series
Link to join seminar: Hosted on Zoom
Optimal portfolio choice under endogenous permanent market impacts
We study the expected utility maximization problem of a large investor who is allowed to make transactions on a tradable asset in an incomplete financial market with endogenous permanent market impacts. The asset price is assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. We show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) which is equivalent to a highly non-linear backward stochastic partial differential equation (BSPDE). We show existence and uniqueness solutions for FBSDEs in the case where the driver function of the representative market maker grows at least quadratic or the utility function of the large investor falls faster than quadratic or is exponential. Explicit examples are provided when the market is complete or the driver function is positively homogeneous.