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Minimax theorems for American options in incomplete markets without time-consistency [article]

Denis Belomestny, Volker Kraetschmer
<span title="2017-08-29">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures  ...  Our conditions do not rely on the notions of stability under pasting or time-consistency and reveal some unexpected connection between the minimax result and the path properties of the corresponding density  ...  Acknowledgements The authors would like to thank Mikhail Urusov for fruitful discussions and helpful remarks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.08904v1">arXiv:1708.08904v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/grjkaymfzbasvnkt4wa2fggx4y">fatcat:grjkaymfzbasvnkt4wa2fggx4y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200909093517/https://arxiv.org/pdf/1708.08904v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0b/d9/0bd928a74d5b7ac79941aec9e5a583941af71a0c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1708.08904v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Optimal Stopping Under Ambiguity

Frank Riedel
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tol7woxlqjeg5bmzadeg6qrg3e" style="color: black;">Social Science Research Network</a> </i> &nbsp;
Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree.  ...  We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).  ...  We need it when using the Optional Sampling Theorem. This theorem does not hold true without time consistency. (ii) Optimal stopping times are usually not unique.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.1013276">doi:10.2139/ssrn.1013276</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2dngxujdpbd3zdph3537ewksku">fatcat:2dngxujdpbd3zdph3537ewksku</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922023402/https://pub.uni-bielefeld.de/download/1944648/2319760" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a0/70/a070d0aa5a6b5e00c9a44610e4da16c13e117a99.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.1013276"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ssrn.com </button> </a>

Arbitrage, hedging and utility maximization using semi-static trading strategies with American options [article]

Erhan Bayraktar, Zhou Zhou
<span title="2016-02-08">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We first get the fundamental theorem of asset pricing (FTAP). Using the FTAP, we get the dualities for the hedging prices of European and American options.  ...  We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies).  ...  In this paper, we consider a financial market in discrete time consisting of stocks, (path-dependent) European options, and (path-dependent) American options (we also refer to these as hedging options)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.06681v5">arXiv:1502.06681v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/unhb3xxcencqlds3psmabxjm6a">fatcat:unhb3xxcencqlds3psmabxjm6a</a> </span>
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Super-hedging American Options with Semi-static Trading Strategies under Model Uncertainty [article]

Erhan Bayraktar, Zhou Zhou
<span title="2017-06-26">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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 π is given by the supremum over the prices of the American option under randomized models.  ...  A non-compact minimax theorem Below is a minimax theorem without compactness of the underlying sets from Ha (1981) . Theorem A.1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1604.04608v2">arXiv:1604.04608v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pi2b3qr54na6rjyfqdr64qpqfa">fatcat:pi2b3qr54na6rjyfqdr64qpqfa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200827022637/https://arxiv.org/pdf/1604.04608v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/60/e4/60e4d184958a7f3364534207517d50a262a3d12b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1604.04608v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 5066 of Mathematical Reviews Vol. , Issue 98H [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
As an application, a suitable stability property for the price of the American option is established; i.e., they show that the price of an American option in a pure diffusion model can be obtained as the  ...  (H-EOTVO-AN; Budapest) A minimax theorem for two functions. Ann. Univ. Sci. Budapest. Eétvés Sect. Math. 39 (1996), 29-33 (1997).  ... 
<span class="external-identifiers"> </span>
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Page 829 of Mathematical Reviews Vol. , Issue 2000a [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In addition, the chapter presents results about American, Asian and some other exotic options and con- vergence results for the passage from discrete to continuous time models.  ...  Summary: “This paper develops a minimax immunization strategy for an infinite factor interest rate model.  ... 
<span class="external-identifiers"> </span>
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Optimal Stopping With Multiple Priors

<span title="">2009</span> <i title="The Econometric Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tzeeifoj3jgqphcasnbbgoqblq" style="color: black;">Econometrica</a> </i> &nbsp;
We relate the multiple prior theory to the classical setup via a minimax theorem.  ...  For more complex payoff structures like barrier options, model ambiguity can introduce new dependencies in the initial i.i.d. framework.  ...  We need it when we apply the Optional Sampling Theorem. This theorem does not hold true without time consistency. (ii) Optimal stopping times are usually not unique 21 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3982/ecta7594">doi:10.3982/ecta7594</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/muaqnf3do5buxnewuaqhq57kdu">fatcat:muaqnf3do5buxnewuaqhq57kdu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809054906/http://www.ifd.dauphine.fr/fileadmin/mediatheque/IFD/Seminaire_risque/seminaire_risque_2008_09/riedeloptimalstopping.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/81/aa/81aa3287a0b7fe26c772448c8125b3dfacfb6bef.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3982/ecta7594"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

The Duality of Optimal Exercise and Domineering Claims: a Doob-Meyer Decomposition Approach to the Snell Envelope

Farshid Jamshidian
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tol7woxlqjeg5bmzadeg6qrg3e" style="color: black;">Social Science Research Network</a> </i> &nbsp;
It also ties in well with several formulations of a duality in optimal stopping theory, including the minimax duality pricing formula in Rogers [30] and Haugh and Kogan [15] for American and Bermudan options  ...  The perpetual American put is treated by incorporating an approach of [2].  ...  For a reward process Z that does have an optimal stopping time T * , the American option can then properly be defined as the pair (T * , Z T * ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.902634">doi:10.2139/ssrn.902634</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5v74soiqfnhi5fwhd5sr2r2r3e">fatcat:5v74soiqfnhi5fwhd5sr2r2r3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070722000404/http://sc.iam.metu.edu.tr/amamef/papers/Jamshidian_Farshid.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ce/78/ce787475224a33bafb05b95aa5b6326c464adfde.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.902634"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ssrn.com </button> </a>

The duality of optimal exercise and domineering claims: a Doob–Meyer decomposition approach to the Snell envelope

Farshid Jamshidian
<span title="">2007</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tniydh5x6nhxjjdxxqynszrpru" style="color: black;">Stochastics: An International Journal of Probability and Stochastic Processes</a> </i> &nbsp;
It also ties in well with several formulations of a duality in optimal stopping theory, including the minimax duality pricing formula in Rogers [30] and Haugh and Kogan [15] for American and Bermudan options  ...  The perpetual American put is treated by incorporating an approach of [2].  ...  For a reward process Z that does have an optimal stopping time T * , the American option can then properly be defined as the pair (T * , Z T * ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/17442500601051914">doi:10.1080/17442500601051914</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ms5xu4gibevvdth4ib2cjyblu">fatcat:5ms5xu4gibevvdth4ib2cjyblu</a> </span>
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Motion preference learning

Peter Kingston, Magnus Egerstedt
<span title="">2011</span> <i title="IEEE"> Proceedings of the 2011 American Control Conference </i> &nbsp;
., "best motions") for these functions. The approach is demonstrated with an example in which human and synthetic motions are compared.  ...  The result is an efficient minimax estimator for the best possible alternative.  ...  In this work we address techniques both for using empirical measurements to learn cost functions that are consistent with humans' aesthetic preferences, and for generalizing from these preference measurements  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/acc.2011.5991211">doi:10.1109/acc.2011.5991211</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ie26t37bezf73gk42kk5wplkwa">fatcat:ie26t37bezf73gk42kk5wplkwa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120712161358/http://users.ece.gatech.edu/~magnus/Papers/ACC11-Learning.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ff/0b/ff0b6e5dbffe223ca2da3d2ed6f00a82848eba3f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/acc.2011.5991211"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

From Wald to Savage: Homo Economicus Becomes a Bayesian Statistician

Nicola Giocoli
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tol7woxlqjeg5bmzadeg6qrg3e" style="color: black;">Social Science Research Network</a> </i> &nbsp;
A rational agent in an economic model is one who maximizes her subjective expected utility and consistently revises her beliefs according to Bayes's rule.  ...  A couple of tentative answers are also offered, involving the role of the consistency requirement in neoclassical analysis and the impact of the postwar transformation of US business schools.  ...  minimax theorem (von Neumann 1928) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.1944218">doi:10.2139/ssrn.1944218</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uo2pooxc6baw3ge26lrcykus5y">fatcat:uo2pooxc6baw3ge26lrcykus5y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171111004900/https://core.ac.uk/download/pdf/12029946.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5a/01/5a01690bd2a6036d57d5a5bc88156a46439bac41.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2139/ssrn.1944218"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ssrn.com </button> </a>

From Wald to Savage:Homo EconomicusBecomes a Bayesian Statistician

Nicola Giocoli
<span title="2012-11-16">2012</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q76tjewsnvbonmj53ripocij3q" style="color: black;">Journal of the History of the Behavioral Sciences</a> </i> &nbsp;
A rational agent in an economic model is one who maximizes her subjective expected utility and consistently revises her beliefs according to Bayes's rule.  ...  A couple of tentative answers are also offered, involving the role of the consistency requirement in neoclassical analysis and the impact of the postwar transformation of US business schools.  ...  minimax theorem (von Neumann 1928) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jhbs.21579">doi:10.1002/jhbs.21579</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/23165740">pmid:23165740</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o3uikxa5knf5hgrp7waal6bm34">fatcat:o3uikxa5knf5hgrp7waal6bm34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922134504/https://mpra.ub.uni-muenchen.de/34117/1/MPRA_paper_34117.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3d/3c/3d3c3baf6b1fffbc2e560d23c6f4770033405853.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jhbs.21579"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Integer-Valued, Minimax Robust Designs for Estimation and Extrapolation in Heteroscedastic, Approximately Linear Models

Zhide Fang, Douglas P. Wiens
<span title="">2000</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/74tjf7abozfclcxg2wuphjfpba" style="color: black;">Journal of the American Statistical Association</a> </i> &nbsp;
Theorem 3 . 3 For WLS estimation with heteroscedastic errors. we have The minimax design { p i )~~l oc mi 4 / 3 2 / 3 , for P3 has pi li where {mi):=l minimizes(16).  ...  We take equally spaced design points, Journal of the American Statistical Association, September 2000 A simulated annealing algorithm, in general, consists of the following: 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2669464">doi:10.2307/2669464</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/orgh5qszrbh4phouhzzcbjfcyi">fatcat:orgh5qszrbh4phouhzzcbjfcyi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130107093124/http://www.stat.ualberta.ca:80/~wiens/stat578/papers/Fang%20&amp;%20Wiens.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/c6/e5c6dcdc675978a22a3c94e00e340dda65534b9d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2669464"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Integer-Valued, Minimax Robust Designs for Estimation and Extrapolation in Heteroscedastic, Approximately Linear Models

Zhide Fang, Douglas P. Wiens
<span title="">2000</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/74tjf7abozfclcxg2wuphjfpba" style="color: black;">Journal of the American Statistical Association</a> </i> &nbsp;
Theorem 3 . 3 For WLS estimation with heteroscedastic errors. we have The minimax design { p i )~~l oc mi 4 / 3 2 / 3 , for P3 has pi li where {mi):=l minimizes(16).  ...  We take equally spaced design points, Journal of the American Statistical Association, September 2000 A simulated annealing algorithm, in general, consists of the following: 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/01621459.2000.10474272">doi:10.1080/01621459.2000.10474272</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x666tnwz6ne7xkorkcnt443k7m">fatcat:x666tnwz6ne7xkorkcnt443k7m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130107093124/http://www.stat.ualberta.ca:80/~wiens/stat578/papers/Fang%20&amp;%20Wiens.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/c6/e5c6dcdc675978a22a3c94e00e340dda65534b9d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/01621459.2000.10474272"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests

Klaus M. Schmidt
<span title="">1993</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tzeeifoj3jgqphcasnbbgoqblq" style="color: black;">Econometrica</a> </i> &nbsp;
However, player one has the option to mimic a type who always plays D. This minimaxes player two, so ultimately he has to take a best response against it.  ...  This argument provides the intuition for the following theorem.  ... 
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