Abstract. We consider optimal investment policies for irreversible capital investment projects under uncertainty in a monopoly situation and in a Stackelberg leader-follower game. We consider two types of payoffs: lump-sum and cash flows. The decisions are the times to enter into the market. The problems belong to the class of optimal stopping times, for which the right approach is that of variational inequalities (V.I.s). In the case of complete markets, payoffs are expected values with respect to the risk-neutral probability. In the case of incomplete markets, the risk-neutral probability is not defined. We consider an investor maximizing his/her utility function, and we consider the investment in the project as an additional decision, besides portfolio investment and consumption decisions. This decision remains a stopping time, conversely to the portfolio investment and consumption decisions (continuous controls). The game problem raises new difficulties. The leader's V.I. has a nondifferentiable obstacle. The weak formulation of the V.I. handles this difficulty. In some cases, the solution of the V.I. may be continuously differentiable although the obstacle is not. An additional difficulty occurs for lump-sum payoffs in the case of incomplete markets. We cannot compare gains and losses at different times. We propose an alternative approach, using equivalence (indifference) considerations. In the case of payoffs characterized by cash flows, this difficulty does not exist, but an intermediary problem arises which has a nice interpretation as a differential game. The solutions thus obtained for the Stackelberg game are not intuitive. Therefore, competition has important consequences on investment decisions.
This study seeks to address the question if the 2016 U.S. Presidential election and Mr. Donald Trump's path to U.S. presidency affected the stock market returns in China. We do not find conclusive results from three leading stock indices of China, SHCOMP, SZCOMP, and SHSZ300. There is an immediate impact shown in SHSZ300, but not in SHCOMP and SZCOMP. We ascribe this to the impact of less sophisticated investors who dominate the stock market in China and also to that country's censorship of the media wherein the government could effectively either block or downplay the unfavorable information.
In this paper, we examine irreversible investment decisions in duopoly games with a variable economic climate. Integrating timing flexibility, competition, and changes in the economic environment in the form of a cash flow process with regime switching, the problem is formulated as a stopping-time game under Stackelberg leader-follower competition, in which both players determine their respective optimal market entry time. By extending the variational inequality approach, we solve for the free boundaries and obtain optimal investment strategies for each player. Despite the lack of regularity in the leader's obstacle and the cash flow regime uncertainty, the regime-dependent optimal policies for both the leader and the follower are obtained. In addition, we perform comprehensive numerical experiments to demonstrate the properties of solutions and to gain insights into the implications of regime switching.
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