Abstract
AbstractWe study the problem of stopping a Brownian bridgeXin order to maximise the expected value of an exponential gain function. The problem was posed by Ernst and Shepp (2015), and was motivated by bond selling with non-negative prices.Due to the non-linear structure of the exponential gain, we cannot rely on methods used in the literature to find closed-form solutions to other problems involving the Brownian bridge. Instead, we must deal directly with a stopping problem for a time-inhomogeneous diffusion. We develop techniques based on pathwise properties of the Brownian bridge and martingale methods of optimal stopping theory, which allow us to find the optimal stopping rule and to show the regularity of the value function.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference24 articles.
1. Variational inequalities and the pricing of American options
2. [9] Dvoretzky, A. (1967). Existence and properties of certain optimal stopping rules. In Proc. Fifth Berkeley Symp. Math. Statist. Prob., Vol. 1, University of California Press, Berkeley, pp. 441–452.
3. Revisiting a theorem of LA Shepp on optimal stopping;Ernst;Commun. Stoch. Anal.,2015
4. Solving non–linear optimal stopping problems by the method of time–change
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献