On the value of optimal stopping games

We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time for the buyer is guaranteed. The results are illustrated explicitly in two examples.Comment: Published at http://dx.doi.org/10.1214/105051606000000204 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Investment timing under incomplete information

We study the decision of when to invest in an indivisible project whose value is perfectly observable but driven by a parameter that is unknown to the decision maker ex ante. This problem is equivalent to an optimal stopping problem for a bivariate Markov process. Using filtering and martingale techniques, we show that the optimal investment region is characterised by a continuous and non-decreasing boundary in the value/belief state space. This generates path-dependency in the optimal investment strategy. We further show that the decision maker always benefits from an uncertain drift relative to an 'average' drift situation. However, a local study of the investment boundary reveals that the value of the option to invest is not globally increasing with respect to the volatility of the value process

Exercise regions of American options on several assets

In this paper, we study the nonemptiness and the shape of the exercise region of American options written on several assets. Our contribution is threefold. First, we state an analytic theorem which characterizes the nonemptiness of the exercise region. Second, we study a particular class of payoff functions for which we explicitly identify the shape and the asymptotic behavior near maturity of the associated exercise region. Finally, we present additional results which complement the Broadie and Detemple results concerning the valuation of various types of American options on several assets.Optimal stopping, free boundary problems, American options

Technology choice under several uncertainty sources

International audienceWe analyze a model of irreversible investment with two sources of uncertainty. A risk-neutral decision maker has the choice between two mutually exclusive projects under input price and output price uncertainty. We propose a complete study of the shape of the rational investment region and we prove that it is never optimal to invest when the alternative investments generate the same payoff independently of its size. A key feature of this bidimensional degree of uncertainty is thus that the payoff generated by each project is not a sufficient statistic to make a rational investment. In this context, our analysis provides a new motive for waiting to invest: the benefits associated with the dominance of one project over the other. As an illustration, we apply our methodology to power generation under uncertainty

A mind is a terrible thing to change: confirmatory bias in financial markets

This paper studies the impact of the confirmatory bias on financial markets. We propose a model in which some traders may ignore new evidence inconsistent with their favorite hypothesis regarding the state of the world. The confirmatory bias provides a unified rationale for several existing stylized facts, including excess volatility, excess volume, and momentum. It also delivers novel predictions for which we find empirical support using data on analysts’ earnings forecasts: traders update beliefs depending on the sign of past signals and previous beliefs, and, at the stock level, differences of opinion are larger when past signals have different signs