Search

We study a dynamic mean–variance portfolio selection problem with return predictability and trading frictions from price impact. Applying mean-field type control theory, we provide a characterisation of an equilibrium trading strategy for an investor facing stochastic investment opportunities. An explicit equilibrium strategy is derived in terms of the solution to a generalised matrix Riccati differential equation, and a sufficient condition is also provided to ensure the latter's well-posedness. Our solution indicates that the investor should trade gradually towards a target portfolio which accounts for return predictability, price impact and time-consistency. Moreover, an asymptotic analysis around small liquidity costs shows that the investor's target portfolio is an equilibrium portfolio without price impact in the first-order sense, and that her first-order approximated value function does not deteriorate significantly for sufficiently small liquidity costs. Finally, our numerical results demonstrate that the target portfolio is more conservative than an equilibrium portfolio without price impact. [ABSTRACT FROM AUTHOR]

In this article, we provide the first systematic study on the unique existence of the solution of backward stochastic dynamical variational inequalities on a general complete filtered probability space. We also build up a comprehensive analysis of the correspondence between these stochastic variational inequalities (resp. backward stochastic dynamics) and the weak solutions (instead of viscosity ones due to the intrinsic non-local nature of the integral of the gradient involved) of a class of non-local parabolic variational inequalities (resp. parabolic partial differential equations), which is barely touched in the existing literature due to its unconventional setting. [ABSTRACT FROM AUTHOR]