On optimal stopping and free boundary problems

By P. Moerbeke. 1973

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Citations in the corpus

Learning When-to-Treat Policies (2019, methodology): “Finally, in the optimal stopping literature (e.g., Van Moerbeke 1976; Jacka 1991; Mordecki 2002; Goel, Dann, and Brunskill 2017), the treatment choices are binary, and the goal is to optimize for a policy for when to start or stop a treatment.”
Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings (2006, methodology): “use a “Markovian approach;” see [19, 13] for details on the Markovian approach in the”
Optimal multiple stopping time problem (2009, background): “For details, one is referred to El Karoui (1981), Karatzas and Shreve (1998) or Peskir and Shiryaev (2006).”
Evaluation of American strangles (2002, methodology): “This was a natural extension of the Black-Scholes method for European options, and was explored further by Van Moerbeke (1974, 1976).”
American options on assets with dividends near expiry (2002, background): “It also agrees with the root of equation (78) of van Moerbeke (1976) for a ¼ a0 ffiffiffi 2 p .”
Optimal Dynamic Allocation of Attention (2018, methodology): “(44)As far as we know, even in the Wald stopping problem, tractable characterizations are not available for more than two states (Peskir and Shiryaev, 2006).”
Some optimal stopping problems with nontrivial boundaries for pricing exotic options (2001, unknown): “[4], [5], [7], [8], [12] and the references therein).”
The Valuation of American Barrier Options Using the Decomposition Technique (2000, unknown): “…C, in which early exercise is not optimal, and the stopping region, S, in which it is, as follows: C = f(St; t)jG(St; t) > h(St)g; S = f(St; t)jG(St; t) h(St)g As demonstrated in McKean (1965) and van Moerbeke (1976), the American option problem can be converted into a free-boundary problem.”
Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes (2007, background): “The key point to note when solving optimal stopping problems for the jump processes established in [27] and [28] is that the smooth-fit condition at the optimal boundary may break down and then needs replacing by the continuous-fit condition; see also [1] for necessary and sufficient conditions for ”
Laplace transforms and American options (2000, methodology): “Integral equation methods have been used to tackle American options before, including the early work by McKean (1965) and Van Moerbeke (1976) on American calls, the studies by Kim (1990), Jacka (1991) and Carr et al. (1992), all of which looked at the difference between European and American…”
On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function (2011, background): “The choice of α∗ f coincides with what would be obtained by applying the principles of continuous and smooth fit from the theory of optimal stopping (see Peskir and Shiryaev [32], Chapter IV.”
Optimal Stopping and the American Put (1991, background): “…techniques, the ‘well-known’ result that the fair price for the option, regarded as a function of the present stock price and the time horizon, is the (essentially) unique solution to a parabolic free-boundary problem; Theorem 4.2.1 (see, for example, McKean (1965) and Van Moerbeke (1976).”
EARLY DETECTION OF A CHANGE IN POISSON RATE AFTER ACCOUNTING FOR POPULATION SIZE EFFECTS (2011, background): “In addition, we extend our approaches to a general setting with arbitrary probability distributions, as well as to the continuous-time setting involving the multiplicative intensity models for Poisson processes, but further research is needed.”