The concept of a forecast horizon for a given player with respect to the set of equilibria in an abstract dynamic game is defined. Consideration is then given to the case of a stochastic dynamic game with memory-less perfect state information and the Nash equilibrium concept. Sufficient...

This note clarifies some issues dealing with the necessary condition for the optimal terminal time in free terminal time optimal control problems. It is shown that this condition is independent of the other maximum principle conditions and a simple proof is presented. Also the economic...

We consider two control problems on a finite horizon; one stochastic and the other deterministic. In both problems the running cost and the terminal cost are the same. The controllable input in both problems is of an additive nature with cost proportional to the input (which can be both positive...

The method of variational inequalities is a useful theoretical tool in stochastic control, but there are few problems in which this method leads to an explicit solution. We present such a problem drawn from portfolio management. An agent can distribute his wealth between two investments, one...

In this paper we analyse a control‐theoretic model of a country possessing a finite amount of a non‐renewable resource. The country can both consume the indigenous resource and export it. Moreover, a substitute for the indigenous resource is available at a given backstop price. We obtain the...

We address the problem of finding an optimal financing mix of retained earnings and external equity for maximizing the value of a firm subject to random returns. The problem is formulated as a singular stochastic control for a diffusion process, and the value function satisfies a free-boundary...

We consider optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the...

We study infinite-horizon stochastic inventory problems with general demand distributions and piecewise linear concave ordering costs. Such costs arise in the important cases of quantity discounts or multiple suppliers. We consider the case of concave cost involving two linear segments. This...

Two types of quantity discounts are treated in the literature, namely, 'all units' discounts and incremental quantity discounts. In the all units quantity discounts model. the discount applies to every unit purchased. As a result, the total purchase cost is a discontinuous function of the...

This paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous-time Markov process. Problems with control (production) and state (inventory) constraints are treated. It is shown that a unique optimal feedback solution exists. This solution...