Optimal stopping of the maximum process: the maximality principle
نویسندگان
چکیده
منابع مشابه
Optimal Stopping of the Maximum Process: The Maximality Principle
where S = (St)t 0 is the maximum process associated with the one-dimensional time-homogeneous diffusion X = (Xt)t 0 , the function x 7! c(x) is positive and continuous, and the supremum is taken over all stopping times of X for which the integral has finite expectation. It is proved, under no extra conditions, that this problem has a solution, i.e. the payoff is finite and there is an optimal s...
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Attention is drawn to the fact that copyright of this thesis rests with its author. This copy of the thesis has been supplied on the condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without the prior written consent of the author. This thesis may be ...
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The maximality principle [6] is shown to be valid in some examples of discounted optimal stopping problems for the maximum process. In each of these examples explicit formulas for the value functions are derived and the optimal stopping times are displayed. In particular, in the framework of the Black-Scholes model, the fair prices of two lookback options with infinite horizon are calculated. T...
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This paper concerns an optimal stopping problem driven by the running maximum of a spectrally negative Lévy process X. More precisely, we are interested in capped versions of the American lookback optimal stopping problem (Gapeev in J. Appl. Probab. 44:713–731, 2007; Guo and Shepp in J. Appl. Probab. 38:647–658, 2001; Pedersen in J. Appl. Probab. 37:972–983, 2000), which has its origins in math...
متن کاملOptimal stopping of the maximum process: a converse to the results of Peskir
Peskir, (and also Meilijson and Ob lój) considered the following optimal stopping problem: find, for an increasing function F and a positive function λ, sup τ E [ F (Sτ ) − ∫ τ 0 λ(Bu)du ] , (1) where S is the maximum process of Brownian motion. In this article we are interested in the converse: find, for an increasing function F and a suitable function λ, sup τ E [ ∫ τ 0 λ(Bu)du − F (Sτ ) ] . ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1998
ISSN: 0091-1798
DOI: 10.1214/aop/1022855875