Time-consistent portfolio optimization

Preference heterogeneity and its equilibrium path

“…Reduction experiment is a commonly used validation. Specifically, the SNHQH discount function (1) is designed in such a way that, by controlling parameters, the SNHQH discount function (1) and its nonstandard HJB (8) can simultaneously reduce to those in many papers (e.g., de-Paz et al, 14 de-Paz et al, 15 Karp,11 Marín-Solano and Patxot, 1 Marín-Solano et al, 19 Marín-Solano and Navas, 12 Marín-Solano and Shevkoplyas, 5 Marín-Solano and Navas, 13 Peng and Hager, 20 Peng and Hager 21 ). Both these papers and the present article use a game-theoretic approach in the sense that no functional assumption has been imposed.…”

“…One is a direct adaption of a discount function (e.g., Equation (10) of the present article). Another is a change of variable (e.g., equation 3.8 in Peng and Kloeden 21 ). The objective functions (7) subjects to { dX(s) = (X(s), u(s), s) ds + (X(s), u(s), s) dz…”

“…B6. Reduction to the SHQH discount function and its HJB (i) The SHQH discount function 21,38 at time t used to evaluate a payoff at time s is…”