Summary We compare projection methods with the standard value function grid algorithm in order to solve overlapping generations models. We apply the methods to a particular 60-period OLG model with elastic labor supply in order to study the effects of unfunded public pensions on aggregate...

An important problem of collective non-ruin is the estimation of the probabilities R(z,t) and R(z) of the finite and ultimate non-ruin, respectively, where t is time and z the initial reserve. The governing equations are first-order Volterra integro-differential equations, partial (PVIDEs) in...

This chapter is concerned with numerical simulation of dynamic economic models. We focus on some basic algorithms and assess their accuracy and stability properties. This analysis is useful for an optimal implementation and testing of these procedures, as well as to evaluate their performance....

Many problems in modern financial economics involve the solution of continuous-time, continuous-state stochastic control problems. Since explicit solutions of such problems are extremely rare, efficient numerical methods are called for. The Markov chain approximation approach provides a class of...

This chapter is concerned with numerical simulation of dynamic economic models. We focus on some basic algorithms and study their accuracy and stability properties. This analysis is useful for an optimal implementation and testing of these procedures, as well as to evaluate their performance....

With constrained portfolios, contingent claims do not generally have a unique price, for which there are no arbitrage opportunities. We generalize earlier results of El Karoui and Quenez (1995) and Cvitanic and Karatzas (1993) by showing that there is an interval of no-arbitrage prices, when...

We solve a model of time to build, in closed form, for the special case where the only option is commencing investment. The ratio of the optimal to the NPV investment threshold is as in the standard analysis of irreversible investment. We then report numerical solutions for the general case...