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 study a renewal theory approach to perpetual two-state switching problems with infinite value functions. Since the corresponding value functions are infinite, the problems fall outside the standard class of problems which can be analyzed using dynamic programming. Instead, we propose an alternative formulation of optimal switching theory in which optimality of a strategy is defined in terms of its long-term mean return, which can be determined using renewal theory. The approach is illustrated by examples in connection with trend-following strategies in finance.

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected backward stochastic differential equations with interconnected barriers, we show that this game has a value and an equilibrium in the players’ switching controls.

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differential equations. This theory is then demonstrated numerically for the special cases of cancellable call and put options in a Black‒Scholes market.

In this paper we study a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward, and signed (positive and negative) switching costs. Using optimal stopping theory for discrete-parameter stochastic processes, we extend a well-known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switching costs.