One attractive objective for a pensioner using the income drawdown option is to minimise the deviation of the pension fund from a prescribed deterministic target. Typically, this problem is formulated as a linear-quadratic optimal control problem, which has the shortcoming that over-performance...

This paper, using the different alternative methods of dynamic optimization (the Lagrange/Kuhn-Tucker (LKT) method, the substitution method, the Hamiltonian method, and the dynamic programming approach) derives the conditions that must be satisfied by the solution to the so-called Ramsey...

We consider a neoclassical growth model with quasi-hyperbolic discounting under Kantian optimization: each temporal self acts in a way that they would like every future self to act. We introduce the notion of a Kantian policy as an outcome of Kantian optimization in a given class of policies. We...

Economists who want to numerically approximate an elaborate dynamic stochastic programming problem (DSPP), either for structural estimation or policy evaluation purposes, are often confined by the curse of dimensionality: richer models with various state and control variables cannot be solved on...

Models of consumer learning and inventory behavior have both proven to be valuable for explaining consumer choice dynamics. In their pure form these models assume consumers solve complex dynamic programming (DP) problems to determine optimal choices. For this reason, these models are best viewed...

We propose two modifications to the method of endogenous grid points that greatly decreases the computational time for life cycle models with many exogenous state variables. First, we use simulated stochastic grids on the exogenous state variables. Second, when we interpolate to find the...

In an incomplete market we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein-Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton-Jacobi-Bellman equation and provide a suitable verification theorem....

Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous time model. We consider the version of recursive utility which gives the most unambiguous separation of risk...

This paper investigates extensions of the method of endogenous gridpoints (ENDGM) introduced by Carroll (2006) to higher dimensions with more than one continuous endogenous state variable. We compare three different categories of algorithms: (i) the conventional method with exogenous grids...

Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous-time model. We use the stochastic maximum principle to analyze the model. This method uses forward/backward...