Optimal Stopping for Partial Sums
Reads0
Chats0
TLDR
In this article, it was shown that the optimal expected return is finite, and conditions under which the optimal stopping times exist, and the supremum is taken over all stop rules.Abstract:
We determine $\sup E\lbrack r(S_T)\rbrack$, where $S_n$ is a sequence of partial sums of independent identically distributed random variables, for two reward functions: $r(x) = x^+$ and $r(x) = (e^x - 1)^+$. The supremum is taken over all stop rules $T$. We give conditions under which the optimal expected return is finite. Under these conditions, optimal stopping times exist, and we determine them. The problem has an interpretation in an action timing problem in finance.read more
Citations
More filters
Book
Introductory Lectures on Fluctuations of Lévy Processes with Applications
TL;DR: In this paper, the authors present decompositions of the paths of Levy processes in terms of their local maxima and an understanding of their short-and long-term behaviour.
BookDOI
Fluctuations of Lévy Processes with Applications
TL;DR: In this article, Kloeden, P., Ombach, J., Cyganowski, S., Kostrikin, A. J., Reddy, J.A., Pokrovskii, A., Shafarevich, I.A.
Journal ArticleDOI
Russian and American put options under exponential phase-type Lévy models
TL;DR: In this article, an explicit expression for the price in the dense class of Levy processes with phase-type jumps in both directions is given for the American put and Russian option (46,47,22) with the stock price modelled as an exponential Levy process.
Journal ArticleDOI
Optimal stopping and perpetual options for Lévy processes
TL;DR: A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formulas for perpetual American put options involving the infimum of the after-mentioned process are obtained.
Journal ArticleDOI
Some remarks on first passage of Lévy processes, the American put and pasting principles
Larbi Alili,Andreas E. Kyprianou +1 more
TL;DR: In this paper, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. Appl. Fin.
References
More filters
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Journal ArticleDOI
Théorie de la spéculation
TL;DR: In this article, Gauthier-Villars implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Journal ArticleDOI
The random character of stock market prices
TL;DR: This paper showed that the text, first written in 1964, is still relevant and relevant at the beginning of the 21st century, which is known to a generation of financial economists having marked the beginnings of the field known as financial econometrics.
With an appendix by
TL;DR: Van Dyke as mentioned in this paper measured the potentials at which viscous jets or drops first appear in a parallel electric field and compared with calculations of A. B. Basset and found that their stability is due to mechanical rather than electrical causes, like a stretched string, which is straight when pulled but bent when pushed.