SSRN Author: Hideyuki TakadaHideyuki Takada SSRN Content
https://www.ssrn.com/author=587304
https://www.ssrn.com/rss/en-usWed, 03 Jul 2019 01:18:20 GMTeditor@ssrn.com (Editor)Wed, 03 Jul 2019 01:18:20 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral TheoryGeometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the d
https://www.ssrn.com/abstract=2644756
https://www.ssrn.com/1802835.htmlSun, 30 Jun 2019 07:56:00 GMTREVISION: Credit Bubbles in Arbitrage Markets: The Geometric Arbitrage Approach to Credit RiskWe apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition for corporate bonds, as well as the generic dynamics for credit market allowing for arbitrage possibilities. Moreover, arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed for the market dynamics minimizing the arbitrage.
https://www.ssrn.com/abstract=2459369
https://www.ssrn.com/1802834.htmlSun, 30 Jun 2019 07:44:32 GMTREVISION: When Risks and Uncertainties Collide: Quantum Mechanical Formulation of Mathematical Finance for Arbitrage MarketsGeometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself.<br><br>The asset and market portfolio dynamics have a quantum mechanical description, which is constructed by quantizing the deterministic version of the stochastic Lagrangian system describing a market allowing for arbitrage.<br><br>Results, obtained by solving explicitly the Schrödinger equations by means of spectral decomposition of the Hamilton operator, coincides with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency. Arbitrage bubbles are computed.
https://www.ssrn.com/abstract=3404437
https://www.ssrn.com/1802833.htmlSun, 30 Jun 2019 07:43:05 GMTREVISION: The Black-Scholes Equation in Presence of ArbitrageWe apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation.<br><br>First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. As a by-product we provide a geometric characterization of the (NUPBR) condition given by the zero curvature (ZC) condition. Finally, we extend the Black-Scholes PDE to markets allowing arbitrage.
https://www.ssrn.com/abstract=2887425
https://www.ssrn.com/1802349.htmlFri, 28 Jun 2019 07:45:10 GMTREVISION: Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral TheoryGeometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the d
https://www.ssrn.com/abstract=2644756
https://www.ssrn.com/1801820.htmlWed, 26 Jun 2019 19:44:25 GMTREVISION: The Black-Scholes Equation in Presence of ArbitrageWe apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation.<br><br>First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. As a by-product we provide a geometric characterization of the (NUPBR) condition given by the zero curvature (ZC) condition. Finally, we extend the Black-Scholes PDE to markets allowing arbitrage.
https://www.ssrn.com/abstract=2887425
https://www.ssrn.com/1801819.htmlWed, 26 Jun 2019 19:43:45 GMTREVISION: When Risks and Uncertainties Collide: Mathematical Finance for Arbitrage Markets in a Quantum Mechanical ViewGeometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself.<br><br>The asset and market portfolio dynamics have a quantum mechanical description, which is constructed by quantizing the deterministic version of the stochastic Lagrangian system describing a market allowing for arbitrage.<br><br>Results, obtained by solving explicitly the Schrödinger equations by means of spectral decomposition of the Hamilton operator, coincides with those obtained by solving the stochastic Euler Lagrange equations derived by a variational principle and providing therefore consistency. Arbitrage bubbles are computed.
https://www.ssrn.com/abstract=3404437
https://www.ssrn.com/1799998.htmlThu, 20 Jun 2019 18:08:27 GMTREVISION: The Black-Scholes Equation in Presence of ArbitrageWe apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation.<br><br>First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. As a by-product we provide a geometric characterization of the (NUPBR) condition given by the zero curvature (ZC) condition. Finally, we extend the Black-Scholes PDE to markets allowing arbitrage.
https://www.ssrn.com/abstract=2887425
https://www.ssrn.com/1799631.htmlThu, 20 Jun 2019 10:30:19 GMTREVISION: Credit Bubbles in Arbitrage Markets: The Geometric Arbitrage Approach to Credit RiskWe apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation.<br>We obtain closed form equations involving default intensities and loss given defaults characterizing the no-free-lunch-with-vanishing-risk condition for corporate bonds, as well as the generic dynamics for credit market allowing for arbitrage possibilities. Moreover, arbitrage credit bubbles for both base credit assets and credit derivatives are explicitly computed for the market dynamics minimizing the arbitrage.
https://www.ssrn.com/abstract=2459369
https://www.ssrn.com/1798772.htmlTue, 18 Jun 2019 01:15:15 GMTREVISION: Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral TheoryGeometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the d
https://www.ssrn.com/abstract=2644756
https://www.ssrn.com/1796536.htmlWed, 12 Jun 2019 10:48:11 GMTREVISION: Can You hear the Shape of a Market? Geometric Arbitrage and Spectral TheoryGeometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the d
https://www.ssrn.com/abstract=2644756
https://www.ssrn.com/1796039.htmlTue, 11 Jun 2019 05:24:31 GMTREVISION: The Black-Scholes Equation in Presence of ArbitrageWe apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation.<br><br>First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. As a by-product we provide a geometric characterization of the (NUPBR) condition given by the zero curvature (ZC) condition. Finally, we extend the Black-Scholes PDE to markets allowing arbitrage.
https://www.ssrn.com/abstract=2887425
https://www.ssrn.com/1780641.htmlThu, 18 Apr 2019 06:34:37 GMT