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Riedel Frank - One of the best experts on this subject based on the ideXlab platform.
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A Knightian irreversible investment problem
'Elsevier BV', 2022Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. A Knightian irreversible investment problem. Journal of Mathematical Analysis and Applications. 2022;507(1): 125744.In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic Backward Equation under the worst-case scenario. In a time-homogeneous setting – where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called “κ-ignorance” – we are able to provide the explicit form of the optimal irreversible investment plan
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Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty
Center for Mathematical Economics, 2020Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty. Center for Mathematical Economics Working Papers. Vol 641. Bielefeld: Center for Mathematical Economics; 2020.We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent's preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a Backward Equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.MSC classification: 93E20, 91B42, 60H30, 65C3
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A Knightian Irreversible Investment Problem
Center for Mathematical Economics, 2020Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. A Knightian Irreversible Investment Problem. Center for Mathematical Economics Working Papers. Vol 634. Bielefeld: Center for Mathematical Economics; 2020.In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic Backward Equation under the worst- case scenario. In a time-homogeneous setting { where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called "\$\kappa$ --ignorance" - we are able to provide the explicit form of the optimal irreversible investment plan.MSC2010 subject classification: 93E20, 91B38, 65C3
Ferrari Giorgio - One of the best experts on this subject based on the ideXlab platform.
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A Knightian irreversible investment problem
'Elsevier BV', 2022Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. A Knightian irreversible investment problem. Journal of Mathematical Analysis and Applications. 2022;507(1): 125744.In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic Backward Equation under the worst-case scenario. In a time-homogeneous setting – where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called “κ-ignorance” – we are able to provide the explicit form of the optimal irreversible investment plan
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Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty
Center for Mathematical Economics, 2020Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty. Center for Mathematical Economics Working Papers. Vol 641. Bielefeld: Center for Mathematical Economics; 2020.We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent's preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a Backward Equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.MSC classification: 93E20, 91B42, 60H30, 65C3
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A Knightian Irreversible Investment Problem
Center for Mathematical Economics, 2020Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. A Knightian Irreversible Investment Problem. Center for Mathematical Economics Working Papers. Vol 634. Bielefeld: Center for Mathematical Economics; 2020.In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic Backward Equation under the worst- case scenario. In a time-homogeneous setting { where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called "\$\kappa$ --ignorance" - we are able to provide the explicit form of the optimal irreversible investment plan.MSC2010 subject classification: 93E20, 91B38, 65C3
Reiichiro Kawai - One of the best experts on this subject based on the ideXlab platform.
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local asymptotic normality property for ornstein uhlenbeck processes with jumps under discrete sampling
Journal of Theoretical Probability, 2013Co-Authors: Reiichiro KawaiAbstract:We address the issue of the local asymptotic normality property and the Fisher information for three characterizing parameters of Ornstein–Uhlenbeck processes with jumps under low frequency and high frequency discrete sampling with expanding observation window. The martingale method with the Kolmogorov Backward Equation and the Malliavin calculus are employed to derive explicit formulas for derivatives of the likelihood ratio function in the form of conditional expectation, which serve as essential tools for justifying the passage to the limit by the dominated convergence theorem. This approach makes it possible to carry out the proof without specifying the law of the jump component and without knowing the tail behaviors of the transition probability density and, as a consequence, to keep various types of jump structure within the scope of this article. The Fisher information under high-frequency sampling is essentially identical to the one for purely Gaussian Ornstein–Uhlenbeck processes due to the dominance of the Gaussian component over the jump component in the short time framework.
Shige Peng - One of the best experts on this subject based on the ideXlab platform.
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mean field Backward stochastic differential Equations a limit approach
Annals of Probability, 2009Co-Authors: Rainer Buckdahn, Boualem Djehiche, Juan Li, Shige PengAbstract:Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to investigate a special mean-field problem in a purely stochastic approach: for the solution (Y, Z) of a mean-field Backward stochastic differential Equation driven by a forward stochastic differential of McKean-Vlasov type with solution X we study a special approximation by the solution (X-N, Y-N, Z(N)) of some decoupled forward-Backward Equation which coefficients are governed by N independent copies of (X-N, Y-N, Z(N)). We show that the convergence speed of this approximation is of order 1/root N. Moreover, our special choice of the approximation allows to characterize the limit behavior of root N(X-N - X, Y-N - Y, Z(N) - Z). We prove that this triplet converges in law to the solution of some forward-Backward. stochastic differential Equation of mean-field type, which is not only governed by a Brownian motion but also by an independent Gaussian field.
Li Hanwu - One of the best experts on this subject based on the ideXlab platform.
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A Knightian irreversible investment problem
'Elsevier BV', 2022Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. A Knightian irreversible investment problem. Journal of Mathematical Analysis and Applications. 2022;507(1): 125744.In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic Backward Equation under the worst-case scenario. In a time-homogeneous setting – where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called “κ-ignorance” – we are able to provide the explicit form of the optimal irreversible investment plan
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Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty
Center for Mathematical Economics, 2020Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. Optimal Consumption with Intertemporal Substitution under Knightian Uncertainty. Center for Mathematical Economics Working Papers. Vol 641. Bielefeld: Center for Mathematical Economics; 2020.We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent's preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a Backward Equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.MSC classification: 93E20, 91B42, 60H30, 65C3
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A Knightian Irreversible Investment Problem
Center for Mathematical Economics, 2020Co-Authors: Ferrari Giorgio, Li Hanwu, Riedel FrankAbstract:Ferrari G, Li H, Riedel F. A Knightian Irreversible Investment Problem. Center for Mathematical Economics Working Papers. Vol 634. Bielefeld: Center for Mathematical Economics; 2020.In this paper, we study an irreversible investment problem under Knightian uncertainty. In a general framework, in which Knightian uncertainty is modeled through a set of multiple priors, we prove existence and uniqueness of the optimal investment plan, and derive necessary and sufficient conditions for optimality. This allows us to construct the optimal policy in terms of the solution to a stochastic Backward Equation under the worst- case scenario. In a time-homogeneous setting { where risk is driven by a geometric Brownian motion and Knightian uncertainty is realized through a so-called "\$\kappa$ --ignorance" - we are able to provide the explicit form of the optimal irreversible investment plan.MSC2010 subject classification: 93E20, 91B38, 65C3
