Optimal consumption and investment with Epstein-Zin recursive utility - Holger Kraft; Thomas Seiferling; Frank Thomas Seifried (Goethe University Frankfurt, SAFE - Sustainable Architecture for Finance in Europe, 2016)
We study continuous-time optimal consumption and investment with Epstein-Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton-Jacobi-Bellman equation by a fixed point argument and makes it possible to compute both indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.
Keywords: G11; G12; D52; D91; C61; C68; 330; consumption-portfolio choice; asset pricing; stochastic di erential utility; incomplete markets; fixed point approach; FBSDE