Warin, valuation of a powerplant under production constraints and markets incompleteness. The induced numerical method involves repeated computations of conditional expectations. Homogenization and asymptotics for small transaction costs. Nonequilibrium fluctuations for the ssep with a slow bond erhard, d. A stochastic control approach to noarbitrage bounds given marginals, with an application to lookback options galichon, a. Semantic scholar profile for nizar touzi, with 801 highly influential citations and 161 scientific research papers. Fields institute monographs book 29 thanks for sharing. This paper considers the nonlinear theory of gmartingales as introduced by peng in 16, 17. Finding ebooks booklid booklid download ebooks for free. This paper presents an original probabilistic method for the numerical computations of greeks i. Pdf download introduction to stochastic control theory. To submit students of this mathematician, please use the new data form, noting this mathematicians mgp id of 143549 for the advisor id.
This book collects some recent developments in stochastic control theory with applications to financial mathematics. The martingale optimal transportation problem is motivated by modelindependent bounds for exotic options in financial mathematics. Edu ecole polytechnique d epartement de math ematiques appliqu ees. Option hedging for small investors under liquidity costs. Nizar touzi ecole polytechnique martingale optimal transport and model free hedging abstract. Contents 1 conditional expectation and linear parabolic pdes 5. Superhedging under uncertain volatility quasisure stochastic analysis second order backward sdes theunboundedvolatilitycase repeatpengsconstructionbyconsidering lip. All structured data from the file and property namespaces is available under the creative commons cc0 license. This principle implies that the reachability sets satisfy. From american options to fully nonlinear pdes nizar touzi imperial college london and ecole polytechnique paris july 4, 2007. Branching di usion representation of semilinear pdes and.
From american options to fully nonlinear pdes nizar touzi ecole polytechnique paris pdes and finance workshop kth, stockholm, august 2023, 2007. The main focus of this paper is on the analysis of the small transaction costs asymptotics. To appear in finance and stochastics 12, 3 july 2008, pp. Optimal skorokhod embedding under nitelymany marginal constraints. Dynamic programming for stochastic target problems and. This is the continuoustime version of the modelintroducedbydammon, spatt,andzhangrev. Branching di usion representation of semilinear pdes and monte carlo approximation pierre henrylabord erey nadia oudjane z xiaolu tanx nizar touzixavier warin k march 8, 2016 abstract we provide a representation result of parabolic semilinear pdes, with polynomial nonlinearity, by branching di usion processes. Diffusion model with stochastic volatility and interest rates. Subscribe to this free journal for more curated articles on this topic.
If you have additional information or corrections regarding this mathematician, please use the update form. Stochastic processes and their applications elsevier. Optimal stochastic control, stochastic target problems. A probabillistic numerical method for fully nonlinear pdes nizar touzi ecole polytechnique paris finance and insurance. Professor of operations research and financial engineering, princeton university. An explicit martingale version of the onedimensional. Optimal multiple stopping and valuation of swing options. Optimal stochastic control, stochastic target problems, and backward sde. The greeks formulae, both with respect to initial conditions and for smooth. As such it is an interesting free boundary problem. From american options to fully nonlinear pdes nizar touzi ecole polytechnique paris 65th birthday of wolfgang runggaldier bressanone, july 20, 2007. The parisprinceton lectures in financial mathematics, of which this is the first volume, will, on an annual basis, publish cuttingedge research in selfcontained, expository articles from outstanding established or upcoming. Media in category nizar touzi the following 3 files are in this category, out of 3 total. A stochastic control approach to no arbitrage bounds.
Weformulate acomputationally tractable extension of theclassical merton optimal consumptioninvestment problem to include the capital gains taxes. According to our current online database, nizar touzi has 6 students and 11 descendants. Download free introduction to stochastic control theory book in pdf and epub free download. Optimal skorokhod embedding under nitelymany marginal. Finally, galichon, henrylabord ere and touzi 16, and henrylabord ere, obloj, spoida, and touzi 17 illustrate how the martingale optimal transport approach the work of the author is supported by the erc grant rofirm 321111. Contents 1 conditional expectation and linear parabolic pdes 11. December 2008 abstract following the framework of c. Applications of malliavin calculus to monte carlo methods. Our approach is based on the \it integrationbyparts formula, which lies at the core of the theory of variational stochastic calculus, as developed in the malliavin calculus. Homogenization and asymptotics for small transaction. Differential properties of these sets are studied by the dynamic programming principle which is proved by the jankovvon neumann measurable selection theorem. This paper considers an extension of the merton optimal investment problem to the case where the risky asset is subject to transaction costs and capital gains taxes. Optimal skorokhod embedding under nitelymany marginal constraints gaoyue guo, xiaolu tan, nizar touzi to cite this version. Files are available under licenses specified on their description page.
Optimal stochastic control, stochastic target problems, and backward sde nizar touzi nizar. A martingale representation theorem for this theory is proved by using the techniques and the results established in 20 for the second order stochastic target problems and the second order backward stochastic differential equations. Martingale representation theorem for the gexpectation by. Under this condition, the martingale optimal transport. Soner, halil mete and touzi, nizar, homogenization and asymptotics for small transaction costs march 23, 2012. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle.
Calcul stochastique et finance ecole polytechnique. Complete duality for martingale optimal transport on the line. We consider the classical merton problem of lifetime consumptionportfolio optimization problem with small proportional transaction costs. Formulation and duality motivation quasisure formulation martingale optimal transport nizartouzi ecolepolytechnique,paris ihp,january10,2017 bonanniversaireyann. Citescore values are based on citation counts in a given year e.
Pierre henrylabord ere nizar touzi january 29, 2018 arxiv. American options prices are characterized by the free boundary problem. Touzi, optimal lifetime consumption and investment under drawdown constraint. Option hedging for small investors under liquidity costs umut c. It is clear that in the limit of zero transaction costs, we recover the classical problem of merton 29 and the main interest is on the derivation of the corrections of this obvious limit. Stochastic control, and application to finance nizar touzi nizar. Parisprinceton lectures on mathematical finance 2002. Other topics include the fixed and free time of control, discounted cost, minimizing the average cost per unit time, and optimal stopping. Siam journal on control and optimization, society for industrial and applied mathematics, 2016. A probabillistic numerical method for fully nonlinear pdes. Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Optimal transport and model free hedging martingale transport problem geometry of optimal transport measure the mongekantorovitch optimal transport problem financial interpretation outline.
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