scholarly journals GENERAL DUALITY FOR PERPETUAL AMERICAN OPTIONS

2008 ◽  
Vol 11 (06) ◽  
pp. 545-566 ◽  
Author(s):  
AURÉLIEN ALFONSI ◽  
BENJAMIN JOURDAIN
Keyword(s):  
Optimal Strategy ◽  
American Options ◽  
Analytical Form ◽  
European Options ◽  
General Duality

In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at ) for perpetual American options when the Call-Put payoff (y - x)+ is replaced by ϕ(x,y). It turns out that the duality still holds under monotonicity and concavity assumptions on ϕ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for European options. Last, we give some examples for which the optimal strategy is known explicitly.

scholarly journals SUPER-HEDGING AMERICAN OPTIONS WITH SEMI-STATIC TRADING STRATEGIES UNDER MODEL UNCERTAINTY

2017 ◽  
Vol 20 (06) ◽  
pp. 1750036 ◽  
Author(s):  
ERHAN BAYRAKTAR ◽  
ZHOU ZHOU
Keyword(s):  
Discrete Time ◽  
Model Uncertainty ◽  
American Options ◽  
American Option ◽  
Trading Strategies ◽  
Martingale Measure ◽  
European Options ◽  
Model Based ◽  
Price Formula ◽  
Dynamic Trading

We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price [Formula: see text] is given by the supremum over the prices of the American option under randomized models. That is, [Formula: see text], where [Formula: see text] and the martingale measure [Formula: see text] are chosen such that [Formula: see text] and [Formula: see text] prices the European options correctly, and [Formula: see text] is the price of the American option under the model [Formula: see text]. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.

scholarly journals Pricing the exotic: Path-dependent American options with stochastic barriers

2021 ◽  
Author(s):  
Alejandro Rojas-Bernal ◽  
Mauricio Villamizar-Villegas
Keyword(s):  
Risk Factors ◽  
Monte Carlo ◽  
Analytical Solution ◽  
American Options ◽  
Pricing Strategy ◽  
Computational Time ◽  
European Options ◽  
Standard Methods ◽  
Path Dependent ◽  
Closed Form Approximation

We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highlight that our estimation requires less than 1% of the computational time compared to other standard methods, such as Monte Carlo simulations.

AMERICAN OPTIONS WITH REGIME SWITCHING

2002 ◽  
Vol 05 (05) ◽  
pp. 497-514 ◽  
Author(s):  
JOHN BUFFINGTON ◽  
ROBERT J. ELLIOTT
Keyword(s):  
Markov Chain ◽  
Finite Number ◽  
Regime Switching ◽  
Hidden Markov ◽  
American Options ◽  
Hidden Markov Chain ◽  
European Options ◽  
Black Scholes

A Black-Scholes market is considered in which the underlying economy, as modeled by the parameters and volatility of the processes, switches between a finite number of states. The switching is modeled by a hidden Markov chain. European options are priced and a Black-Scholes equation obtained. The approximate valuation of American options due to Barone-Adesi and Whaley is extended to this setting.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

Automated Development of Clinical Strategies Using Multistage Decision Analysis

1986 ◽  
Vol 25 (04) ◽  
pp. 207-214 ◽  
Author(s):  
P. Glasziou
Keyword(s):  
Decision Tree ◽  
Decision Analysis ◽  
Decision Trees ◽  
Optimal Strategy ◽  
Cholestatic Jaundice ◽  
Clinical Strategies ◽  
Simultaneous Study

SummaryThe development of investigative strategies by decision analysis has been achieved by explicitly drawing the decision tree, either by hand or on computer. This paper discusses the feasibility of automatically generating and analysing decision trees from a description of the investigations and the treatment problem. The investigation of cholestatic jaundice is used to illustrate the technique.Methods to decrease the number of calculations required are presented. It is shown that this method makes practical the simultaneous study of at least half a dozen investigations. However, some new problems arise due to the possible complexity of the resulting optimal strategy. If protocol errors and delays due to testing are considered, simpler strategies become desirable. Generation and assessment of these simpler strategies are discussed with examples.

SH-Wave Scattering From the Interface Defect

2017 ◽  
Vol 5 (1) ◽  
pp. 45-50
Author(s):  
Myron Voytko ◽  
◽  
Yaroslav Kulynych ◽  
Dozyslav Kuryliak
Keyword(s):  
Half Space ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elastic Layer ◽  
Analytical Form ◽  
Structure Parameters ◽  
Sh Wave ◽  
Interface Defect ◽  
Hopf Method

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

Irritable bowel syndrome and probiotics place in therapeutic strategies

Infectio ro ◽  
2018 ◽  
Vol 56 (4) (1) ◽  
pp. 9-21
Author(s):  
Ștefan-Sorin Aramă
Keyword(s):  
Irritable Bowel Syndrome ◽  
Optimal Strategy ◽  
Vitamin B6 ◽  
Scientific Evidence ◽  
Bifidobacterium Longum ◽  
Lactobacillus Rhamnosus ◽  
Therapeutic Strategies ◽  
Intestinal Dysbiosis ◽  
Irritable Bowel ◽  
The Moment

Irritable bowel syndrome is a frequent digestive condition, with an unclear etiopathogeny. Very probably intestinal dysbiosis plays an important role. For the moment there are no guidelines for treatment. There is scientific evidence for several therapies: modification of diet, non-resorbable antibiotics (rifaximin-α) and probiotics. Giving probiotics after each antibiotic course (an association of Bifidobacterium longum BB536 and Lactobacillus rhamnosus HN001) supplemented with vitamin B6 may be an optimal strategy.

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