We solve non-Markovian optimal switching problems in discrete time on an infinite horizon, when the decision-maker is risk-aware and the filtration is general, and establish existence and uniqueness of solutions for the associated reflected backward stochastic difference equations. An example application to hydropower planning is provided.

We consider infinite-horizon optimal control problems. The main idea is to convert the problem into an equivalent finite-horizon nonlinear optimal control problem. The resulting problem is then solved by means of a direct method using Haar wavelets. A local property of Haar wavelets is applied to simplify the calculation process. The accuracy of the present method is demonstrated by two illustrative examples.

In this work we study the structure of approximatesolutions of autonomous variational problems with a lowersemicontinuous strictly convex integrand f : Rn ×Rn $\to$ R 1 $\cup$ $\{\infty\}$ , where Rn is the n-dimensional Euclideanspace. We obtain a full description of the structure of theapproximate solutions which is independent of the length of theinterval, for all sufficiently large intervals.

Even over a 75-year horizon, forecasts of PAYGO pension finances are misleadingly optimistic. Infinite horizon forecasts are necessary, but are they possible? We build on earlier stochastic forecasts of the US Social Security trust fund which model key demographic and economic variables as historical time series, and use the fitted models to generate Monte Carlo simulations of future fund performance. Using a 500-year stochastic projection, effectively infinite with discounting, we find a fund balance of −5.15 per cent of payroll, compared to the −3.5 per cent of the 2004 Trustees‘ Report, probably reflecting different mortality projections. Our 95 per cent probability bounds are −10.5 and −1.3 per cent. Such forecasts, which reflect only ‘routine’ uncertainty, have many problems but nonetheless seem worthwhile.

Turnpike theorems deal with the optimality of trajectories reaching asingular solution, in calculus of variations oroptimal control problems.For scalar calculus of variations problems in infinite horizon, linear withrespect to the derivative, we use the theory of viscosity solutions ofHamilton-Jacobi equations to obtain a unique characterization of the valuefunction.With this approach, we extend for the scalar case the classical result based onGreen theorem, when there is uniqueness of the singular solution.We provide a new necessary and sufficient condition for turnpikeoptimality, even in the presence of multiple singular solutions.