This paper focuses on the possibility that financial markets require risk premia on holding sovereign debt of countries that appear vulnerable from a fiscal sustainability perspective. Both the level of debt as well as the rate of change of debt are assumed to impact on the risk premium. We analyze the impact of such an endogenous risk premium in a simple debt game between a monetary and a fiscal player, as introduced by [Tabellini (1986) Journal of Economic Dynamics and Control 10, 427–442]. The risk premium term adds a nonlinearity to the linear model in case risk premia are absent. We analyze outcomes in case of noncooperative open-loop Nash strategies and in case of cooperative strategies and consider the workings of the risk premium as a market-based disciplining device (in case of high debt) and adjustment rewarding device (in case of a declining debt trajectory).

An aging population in modern societies has put stress on public pension systems. To prevent social security deficits from increasing to unbounded levels of public debt we focus on two policies: reducing the generosity of pension benefits, determined by the government, and postponing the effective retirement age, chosen by employees. An atomistic employee would disregard the effect of his retirement decision on the public debt and would retire as soon as possible. Conversely, an ideal farsighted agency considering all current and future employees would postpone retirement, thereby alleviating the pressure on public debt and allowing a more generous long-run pension. The government may design a proper incentive strategy to induce myopic atomistic decision makers to act nonmyopically. This strategy is a two-part incentive with nonlinear dependence on the stock of public debt. It is credible if deceiving employees slightly adjust their retirement-age decisions to increments in the public debt.

We study here the impulse control minimax problem. We allow the cost functionals anddynamics to be unbounded and hence the value functions can possibly be unbounded. We provethat the value function of the problem is continuous. Moreover, the value function ischaracterized as the unique viscosity solution of an Isaacs quasi-variational inequality.This problem is in relation with an application in mathematical finance.

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacsoperators. We establish such an estimate for the parabolic Cauchy problem in the wholespace  [0, +∞) × ℝn and, under some periodicity and eitherellipticity or controllability assumptions, we deduce a similar estimate for the ergodicconstant associated to the operator. An interesting byproduct of the latter result will bethe local uniform convergence for some classes of singular perturbation problems.

We consider a model for the control of a linear network flow system with unknown but bounded demandand polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective functionthat makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.

We study the asymptotic behavior of $\lambda v_\lambda$ as $\lambda\rightarrow 0^+$ , where $v_\lambda$ is the viscosity solution of the following Hamilton-Jacobi-Isaacs equation (infinite horizon case) \[ \lambda v_\lambda + H(x,Dv_\lambda)=0,\] with \[H(x,p):=\min_{b\in B}\max_{a \in A} \{-f(x,a,b)\cdot p -l(x,a,b)\}.\] We discuss the cases in which the state of the system is required to stay in an n-dimensional torus, called periodic boundary conditions,or in the closure of a bounded connected domain $\Omega\subset{\xR}^n$ with sufficiently smooth boundary. As far as the latter is concerned, we treat boththe case of the Neumann boundary conditions(reflection on the boundary) andthe case of state constraints boundary conditions.Under the uniform approximate controllability assumption of one player, we extendthe uniform convergence result of the value function to a constant as $\lambda\rightarrow 0^+$ to differential games.As far as state constraints boundary conditions are concerned, we give an example where the value function is Hölder continuous.