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Ronnie Sircar - One of the best experts on this subject based on the ideXlab platform.
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Special issue dedicated to the 2011 Humboldt–Princeton Workshop on Mathematical Finance
Mathematics and Financial Economics, 2013Co-Authors: Ulrich Horst, Ronnie SircarAbstract:The 3rd Humboldt–PrincetonWorkshopwas held in Berlin on October 28–29th, 2011, bringing together Mathematicians, Economists and Statisticians for a lively and stimulating meeting. The four papers in this special issue reflect some of the diversity and interesting problems presented and discussed at the workshop. The first paper, byReneCarmona and Francois Delarue, analyzes the connections between Mean Field Games and the McKean–Vlasov equation, motivated by application to cap-andtrade models for greenhouse gas emissions, and using techniques of backward stochastic differential equations. The second paper, by Rene Carmona, Michael Coulon and Daniel Schwarz, is on the topic of electricity markets and understanding how their dynamics arises from the order in which energy is supplied from different fuel sources. The structural model developed here is used to provide tractable formulas for electricity forward contracts and spread options. The third paper, by Zorana Grbac and Antonis Papapantoleon, constructs an analytically tractable gramework for modeling the LIBOR interest rates while incorporating default risk. This is based on the theory of affine processes, and the authors highlight the application to valuing CDS spreads and counterparty risk. The final paper, by Andreas Hamel, Birgit Rudloff and Mihaela Yankova, studies construction and computation of a family of set-valued riskmeasures, that can be used to quantify the risk of portfolios that contain assets in different currencies, for instance. In this paper, the mathematics and numerical issues are illustrated with the set-valued average value at risk measure. The papers cover a wide range of topics in Mathematical Finance and were a pleasure for us, as guest editors, to read.We thank the participants of the Humboldt–PrincetonWorkshop,
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special issue dedicated to the 2011 humboldt princeton workshop on Mathematical Finance
Mathematics and Financial Economics, 2013Co-Authors: Ulrich Horst, Ronnie SircarAbstract:The 3rd Humboldt–PrincetonWorkshopwas held in Berlin on October 28–29th, 2011, bringing together Mathematicians, Economists and Statisticians for a lively and stimulating meeting. The four papers in this special issue reflect some of the diversity and interesting problems presented and discussed at the workshop. The first paper, byReneCarmona and Francois Delarue, analyzes the connections between Mean Field Games and the McKean–Vlasov equation, motivated by application to cap-andtrade models for greenhouse gas emissions, and using techniques of backward stochastic differential equations. The second paper, by Rene Carmona, Michael Coulon and Daniel Schwarz, is on the topic of electricity markets and understanding how their dynamics arises from the order in which energy is supplied from different fuel sources. The structural model developed here is used to provide tractable formulas for electricity forward contracts and spread options. The third paper, by Zorana Grbac and Antonis Papapantoleon, constructs an analytically tractable gramework for modeling the LIBOR interest rates while incorporating default risk. This is based on the theory of affine processes, and the authors highlight the application to valuing CDS spreads and counterparty risk. The final paper, by Andreas Hamel, Birgit Rudloff and Mihaela Yankova, studies construction and computation of a family of set-valued riskmeasures, that can be used to quantify the risk of portfolios that contain assets in different currencies, for instance. In this paper, the mathematics and numerical issues are illustrated with the set-valued average value at risk measure. The papers cover a wide range of topics in Mathematical Finance and were a pleasure for us, as guest editors, to read.We thank the participants of the Humboldt–PrincetonWorkshop,
Jean-francois Berret - One of the best experts on this subject based on the ideXlab platform.
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A Mathematical Finance approach to the stochastic and intermittent viscosity fluctuations in living cells
Soft matter, 2020Co-Authors: Claude Bostoen, Jean-francois BerretAbstract:Here we report on the viscosity of eukaryotic living cells, as a function of time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblast cells are investigated using an active microrheological technique, where the magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in Mathematical Finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1–10 s and 100–200 s, not previously disclosed. The shorter time is found to be related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and the statistical results from a Mathematical Finance approach. The current approach could be exploited to reveal hidden features from biological complex systems or to determine new biomarkers of cellular metabolism.
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A Mathematical Finance approach to the stochastic and intermittent viscosity fluctuations in living cells
Soft Matter, 2020Co-Authors: Claude Bostoen, Jean-francois BerretAbstract:Here we report on the viscosity of eukaryotic living cells as a function of the time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblastic cells are investigated using an active microrheological technique, where magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in Mathematical Finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1-10 s and 100-200 s, not previously disclosed. The shorter time is found being related to the internal relaxation time of the cy-toplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and statistical results from Mathematical Finance. The current approach could be exploited to reveal hidden features from biological complex systems, or determine new biomarkers of cellular metabolism.
Ulrich Horst - One of the best experts on this subject based on the ideXlab platform.
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Special issue dedicated to the 2011 Humboldt–Princeton Workshop on Mathematical Finance
Mathematics and Financial Economics, 2013Co-Authors: Ulrich Horst, Ronnie SircarAbstract:The 3rd Humboldt–PrincetonWorkshopwas held in Berlin on October 28–29th, 2011, bringing together Mathematicians, Economists and Statisticians for a lively and stimulating meeting. The four papers in this special issue reflect some of the diversity and interesting problems presented and discussed at the workshop. The first paper, byReneCarmona and Francois Delarue, analyzes the connections between Mean Field Games and the McKean–Vlasov equation, motivated by application to cap-andtrade models for greenhouse gas emissions, and using techniques of backward stochastic differential equations. The second paper, by Rene Carmona, Michael Coulon and Daniel Schwarz, is on the topic of electricity markets and understanding how their dynamics arises from the order in which energy is supplied from different fuel sources. The structural model developed here is used to provide tractable formulas for electricity forward contracts and spread options. The third paper, by Zorana Grbac and Antonis Papapantoleon, constructs an analytically tractable gramework for modeling the LIBOR interest rates while incorporating default risk. This is based on the theory of affine processes, and the authors highlight the application to valuing CDS spreads and counterparty risk. The final paper, by Andreas Hamel, Birgit Rudloff and Mihaela Yankova, studies construction and computation of a family of set-valued riskmeasures, that can be used to quantify the risk of portfolios that contain assets in different currencies, for instance. In this paper, the mathematics and numerical issues are illustrated with the set-valued average value at risk measure. The papers cover a wide range of topics in Mathematical Finance and were a pleasure for us, as guest editors, to read.We thank the participants of the Humboldt–PrincetonWorkshop,
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special issue dedicated to the 2011 humboldt princeton workshop on Mathematical Finance
Mathematics and Financial Economics, 2013Co-Authors: Ulrich Horst, Ronnie SircarAbstract:The 3rd Humboldt–PrincetonWorkshopwas held in Berlin on October 28–29th, 2011, bringing together Mathematicians, Economists and Statisticians for a lively and stimulating meeting. The four papers in this special issue reflect some of the diversity and interesting problems presented and discussed at the workshop. The first paper, byReneCarmona and Francois Delarue, analyzes the connections between Mean Field Games and the McKean–Vlasov equation, motivated by application to cap-andtrade models for greenhouse gas emissions, and using techniques of backward stochastic differential equations. The second paper, by Rene Carmona, Michael Coulon and Daniel Schwarz, is on the topic of electricity markets and understanding how their dynamics arises from the order in which energy is supplied from different fuel sources. The structural model developed here is used to provide tractable formulas for electricity forward contracts and spread options. The third paper, by Zorana Grbac and Antonis Papapantoleon, constructs an analytically tractable gramework for modeling the LIBOR interest rates while incorporating default risk. This is based on the theory of affine processes, and the authors highlight the application to valuing CDS spreads and counterparty risk. The final paper, by Andreas Hamel, Birgit Rudloff and Mihaela Yankova, studies construction and computation of a family of set-valued riskmeasures, that can be used to quantify the risk of portfolios that contain assets in different currencies, for instance. In this paper, the mathematics and numerical issues are illustrated with the set-valued average value at risk measure. The papers cover a wide range of topics in Mathematical Finance and were a pleasure for us, as guest editors, to read.We thank the participants of the Humboldt–PrincetonWorkshop,
Nizar Touzi - One of the best experts on this subject based on the ideXlab platform.
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Paris-Princeton Lectures on Mathematical Finance
2010Co-Authors: Jose Scheinkman, Elyès Jouini, René Carmona, Erhan Cinlare, Ivar Ekeland, Nizar TouziAbstract:This is the fourth volume of the Paris-Princeton Lectures in Mathematical Finance. The goal of this series is to publish cutting edge research in self contained articles prepared by established academics or promising young researchers invited by the editors. Contributions are refereed and particular attention is paid to the quality of the exposition, the goal being to publish articles that can serve as introductory references for research. The series is a result of frequent exchanges between researchers in finance and financial mathematics in Paris and Princeton. Many of us felt that the field would benefit from timely exposés of topics in which there is important progress. René Carmona, Erhan Cinlar, Ivar Ekeland, Elyes Jouini, José Scheinkman and Nizar Touzi serve in the first editorial board of the Paris-Princeton Lectures in Financial Mathematics. Although many of the chapters involve lectures given in Paris orPrinceton, we also invite other contributions. Springer Verlag kindly offered to hostthe initiative under the umbrella of the Lecture Notes in Mathematics series, and weare thankful to Catriona Byrne for her encouragement and her help. This fourth volume contains five chapters. In the first chapter, Areski Cousin, Monique Jeanblanc, and Jean -Paul Laurent discuss risk management and hedging of credit derivatives. The latter are over-the-counter (OTC) financial instruments designed to transfer credit risk associated to are ference entity from one counter party to another. The agreement involves a seller and a buyer of protection, the sellerbeing committed to cover the losses induced by the default. The popularity of theseinstruments lead a runaway market of complex derivatives whose risk management did not developas fast. This first chapter fills the gap by providing rigorous tools for quantifying and hedging counterparty risk in some of these markets. In the second chapter, Stéphane Crépey reviews the general theory of for-ward backward stochastic differential equations and their associated systems of partial integro-differential obstacle problems and applies it to pricing and hedging financial derivatives. Motivated by the optimal stopping and optimal stopping game formulations of American option and convertible bond pricing, he discussesthe well-posedness and sensitivities of reflected and doubly reflected Markovian Backward Stochastic Differential Equations. The third part of the paper is devotedto the variational inequality formulation of these problems and to a detailed discussion of viscosity solutions. Finally he also considers discrete path-dependenceissues such as dividend payments. The third chapter written by Olivier Guéant Jean-Michel Lasry and Pierre-Louis Lions presents an original and unified account of the theory and the applications of the mean field games as introduced and developed by Lasry and Lions in a seriesof lectures and scattered papers. This chapter provides systematic studies illustrating the application of the theory to domains as diverse as population behavior (theso-called Mexican wave), or economics (management of exhaustible resources). Some of the applications concern optimization of individual behavior when inter-acting with a large population of individuals with similar and possibly competing objectives. The analysis is also shown to apply to growth models and for example, to their application to salary distributions. The fourth chapter is contributed by David Hobson. It is concerned with the applications of the famous Skorohod embedding theorem to the proofs of model in dependent bounds on the prices of options. Beyond the obvious importance of thefinancial application, the value of this chapter lies in the insightful and extremely pedagogical presentation of the Skorohodem bedding problem and its application to the analysis of martingales with given one-dimensional marginals, providing a one-to-one correspondence between candidate price processes which are consistent with observed call option prices and solutions of the Skorokhod embedding problem, extremal solutions leading to robust model in dependent prices and hedges for exoticoptions. The final chapter is concerned with pricing and hedging in exponential Lévy models. Peter Tankov discusses three aspects of exponential Lévy models: absenceof arbitrage, including more recent results on the absence of arbitrage in multi dimensional models, properties of implied volatility, and modern approaches tohedging in these models. It is a self contained introduction surveying all the results and techniques that need to be known to be able to handle exponential Lévy models in finance.
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Paris-Princeton Lectures on Mathematical Finance 2002
2003Co-Authors: Jose Scheinkman, Elyès Jouini, René Carmona, Erhan Cinlare, Ivar Ekeland, Nizar TouziAbstract:This is the fourth volume of the Paris-Princeton Lectures in Mathematical Finance. The goal of this series is to publish cutting edge research in self contained articles prepared by established academics or promising young researchers invited by the editors. Contributions are refereed and particular attention is paid to the quality of the exposition, the goal being to publish articles that can serve as introductory references for research. The series is a result of frequent exchanges between researchers in finance and financial mathematics in Paris and Princeton. Many of us felt that the field would benefit from timely exposes of topics in which there is important progress. Rene Carmona, Erhan Cinlar, Ivar Ekeland, Elyes Jouini, Jose Scheinkman and Nizar Touzi serve in the first editorial board of the Paris-Princeton Lectures in Financial Mathematics. Although many of the chapters involve lectures given in Paris orPrinceton, we also invite other contributions. Springer Verlag kindly offered to hostthe initiative under the umbrella of the Lecture Notes in Mathematics series, and weare thankful to Catriona Byrne for her encouragement and her help. This fourth volume contains five chapters. In the first chapter, Areski Cousin, Monique Jeanblanc, and Jean -Paul Laurent discuss risk management and hedging of credit derivatives. The latter are over-the-counter (OTC) financial instruments designed to transfer credit risk associated to are ference entity from one counter party to another. The agreement involves a seller and a buyer of protection, the sellerbeing committed to cover the losses induced by the default. The popularity of theseinstruments lead a runaway market of complex derivatives whose risk management did not developas fast. This first chapter fills the gap by providing rigorous tools for quantifying and hedging counterparty risk in some of these markets. In the second chapter, Stephane Crepey reviews the general theory of for-ward backward stochastic differential equations and their associated systems of partial integro-differential obstacle problems and applies it to pricing and hedging financial derivatives. Motivated by the optimal stopping and optimal stopping game formulations of American option and convertible bond pricing, he discussesthe well-posedness and sensitivities of reflected and doubly reflected Markovian Backward Stochastic Differential Equations. The third part of the paper is devotedto the variational inequality formulation of these problems and to a detailed discussion of viscosity solutions. Finally he also considers discrete path-dependenceissues such as dividend payments. The third chapter written by Olivier Gueant Jean-Michel Lasry and Pierre-Louis Lions presents an original and unified account of the theory and the applications of the mean field games as introduced and developed by Lasry and Lions in a seriesof lectures and scattered papers. This chapter provides systematic studies illustrating the application of the theory to domains as diverse as population behavior (theso-called Mexican wave), or economics (management of exhaustible resources). Some of the applications concern optimization of individual behavior when inter-acting with a large population of individuals with similar and possibly competing objectives. The analysis is also shown to apply to growth models and for example, to their application to salary distributions. The fourth chapter is contributed by David Hobson. It is concerned with the applications of the famous Skorohod embedding theorem to the proofs of model in dependent bounds on the prices of options. Beyond the obvious importance of thefinancial application, the value of this chapter lies in the insightful and extremely pedagogical presentation of the Skorohodem bedding problem and its application to the analysis of martingales with given one-dimensional marginals, providing a one-to-one correspondence between candidate price processes which are consistent with observed call option prices and solutions of the Skorokhod embedding problem, extremal solutions leading to robust model in dependent prices and hedges for exoticoptions. The final chapter is concerned with pricing and hedging in exponential Levy models. Peter Tankov discusses three aspects of exponential Levy models: absenceof arbitrage, including more recent results on the absence of arbitrage in multi dimensional models, properties of implied volatility, and modern approaches tohedging in these models. It is a self contained introduction surveying all the results and techniques that need to be known to be able to handle exponential Levy models in finance.
Claude Bostoen - One of the best experts on this subject based on the ideXlab platform.
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A Mathematical Finance approach to the stochastic and intermittent viscosity fluctuations in living cells
Soft matter, 2020Co-Authors: Claude Bostoen, Jean-francois BerretAbstract:Here we report on the viscosity of eukaryotic living cells, as a function of time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblast cells are investigated using an active microrheological technique, where the magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in Mathematical Finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1–10 s and 100–200 s, not previously disclosed. The shorter time is found to be related to the internal relaxation time of the cytoplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and the statistical results from a Mathematical Finance approach. The current approach could be exploited to reveal hidden features from biological complex systems or to determine new biomarkers of cellular metabolism.
-
A Mathematical Finance approach to the stochastic and intermittent viscosity fluctuations in living cells
Soft Matter, 2020Co-Authors: Claude Bostoen, Jean-francois BerretAbstract:Here we report on the viscosity of eukaryotic living cells as a function of the time, and on the application of stochastic models to analyze its temporal fluctuations. The viscoelastic properties of NIH/3T3 fibroblastic cells are investigated using an active microrheological technique, where magnetic wires, embedded into cells, are being actuated remotely. The data reveal anomalous transient responses characterized by intermittent phases of slow and fast rotation, revealing significant fluctuations. The time dependent viscosity is analyzed from a time series perspective by computing the autocorrelation functions and the variograms, two functions used to describe stochastic processes in Mathematical Finance. The resulting analysis gives evidence of a sub-diffusive mean-reverting process characterized by an autoregressive coefficient lower than 1. It also shows the existence of specific cellular times in the ranges 1-10 s and 100-200 s, not previously disclosed. The shorter time is found being related to the internal relaxation time of the cy-toplasm. To our knowledge, this is the first time that similarities are established between the properties of time series describing the intracellular metabolism and statistical results from Mathematical Finance. The current approach could be exploited to reveal hidden features from biological complex systems, or determine new biomarkers of cellular metabolism.
