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  1. Optimal dxecution with multiplicative price impact and incomplete information on the return
    Erschienen: [2022]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of assets in... mehr

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    We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of assets in order to maximize a net expected profit functional, and lump-sum as well as singularly continuous actions are allowed. Our mathematical modelling leads to a singular stochastic control problem featuring a finite-fuel constraint and partial observation. We provide the complete analysis of an equivalent three-dimensional degenerate problem under full information, whose state process is composed of the asset's price dynamics, the amount of available assets in the portfolio, and the investor's belief about the true value of the asset's trend. The optimal execution rule and the problem's value function are expressed in terms of the solution to a truly two-dimensional optimal stopping problem, whose associated belief-dependent free boundary b triggers the investor's optimal selling rule. The curve b is uniquely determined through a nonlinear integral equation, for which we derive a numerical solution allowing to understand the sensitivity of the problem's solution with respect to the relevant model's parameters.

     

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    Sprache: Englisch
    Medientyp: Buch (Monographie)
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    hdl: 10419/273039
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 663 (February 2022)
    Schlagworte: optimal execution problem; multiplicative price impact; singular stochastic control; partial observation; optimal stopping
    Umfang: 1 Online-Ressource (circa 38 Seiten), Illustrationen
  2. A unifying framework for submodular mean field games
    Erschienen: [2022]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to... mehr

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    We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is allowed. The setting is general enough to encompass qualitatively different problems, such as mean field games for discrete time finite space Markov chains, singularly controlled and reflected diffusions, and mean field games of optimal timing. Our analysis hinges on Tarski's fixed point theorem, along with technical results on lattices of flows of probability and sub-probability measures.

     

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    hdl: 10419/249884
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 661 (January 2022)
    Schlagworte: Mean field games; submodularity; complete lattice of measures; Tarski's fixedpoint theorem; Markov chain; singular stochastic control; reflected diffusion; optimal stopping
    Umfang: 1 Online-Ressource (circa 37 Seiten)
  3. Optimal dividend payout under stochastic discounting
    Erschienen: [2021]
    Verlag:  Fondazione Collegio Carlo Alberto, Torino

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    Schriftenreihe: Carlo Alberto notebooks ; no. 661 (October 2021)
    Schlagworte: Optimal dividend; stochastic interest rates; CIR model; singular control; optimal stopping; free boundary problems
    Umfang: 1 Online-Ressource (circa 44 Seiten), Illustrationen
  4. Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon
    Erschienen: [2022]
    Verlag:  CCA, Fondazione Collegio Carlo Alberto, Torino

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    Schriftenreihe: Carlo Alberto notebooks ; no. 677 (January 2022)
    Schlagworte: optimal stopping; free boundary problems; continuous boundary; smooth-fit; local time; one-dimensional diffusions
    Umfang: 1 Online-Ressource (circa 42 Seiten), Illustrationen
  5. Mean-field games of finite-fuel capacity expansion with singular controls
    Erschienen: [2022]
    Verlag:  CCA, Fondazione Collegio Carlo Alberto, Torino

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    Schriftenreihe: Carlo Alberto notebooks ; no. 678 (May 2022)
    Schlagworte: Nash equilibria; mean-field games; singular controls; capacity expansion; goodwill problem; optimal stopping; free boundary problems; Lipschitz free boundary; Skorokhod reflection problem
    Umfang: 1 Online-Ressource (circa 47 Seiten)
  6. Sequential sampling beyond decisions?
    a normative model of decision confidence
    Erschienen: 2022
    Verlag:  Charles University, Center for Economic Research and Graduate Education, Prague

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    Sprache: Englisch
    Medientyp: Ebook
    Format: Online
    ISBN: 9788073435462; 9788073446574
    Schriftenreihe: Working paper series / CERGE-EI ; 739
    Schlagworte: decision; confidence; sequential sampling; optimal stopping
    Umfang: 1 Online-Ressource (circa 43 Seiten), Illustrationen
  7. Uncertainty over uncertainty in environmental policy adoption
    Bayesian larning of unpredictable socioeconomic costs
    Erschienen: [2023]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    The socioeconomic impact of pollution naturally comes with uncertainty due to, e.g., current new technological developments in emissions' abatement or demographic changes. On top of that, the trend of the future costs of the environmental damage is... mehr

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    The socioeconomic impact of pollution naturally comes with uncertainty due to, e.g., current new technological developments in emissions' abatement or demographic changes. On top of that, the trend of the future costs of the environmental damage is unknown: Will global warming dominate or technological advancements prevail? The truth is that we do not know which scenario will be realised and the scientific debate is still open. This paper captures those two layers of uncertainty by developing a real-options-like model in which a decision maker aims at adopting a once-and-for-all costly reduction in the current emissions rate, when the stochastic dynamics of the socioeconomic costs of pollution are subject to Brownian shocks and the drift is an unobservable random variable. By keeping track of the actual evolution of the costs, the decision maker is able to learn the unknown drift and to form a posterior dynamic belief of its true value. The resulting decision maker's timing problem boils down to a truly two-dimensional optimal stopping problem which we address via probabilistic free-boundary methods and a state-space transformation. We show that the optimal timing for implementing the emissions reduction policy is the first time that the learning process has become "decisive" enough; that is, when it exceeds a time-dependent percentage. This is given in terms of an endogenously determined threshold uniquely solving a nonlinear integral equation, which we can solve numerically. We discuss the implications of the optimal policy and also perform comparative statics to understand the role of the relevant model's parameters in the optimal policy.

     

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    Sprache: Englisch
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    Weitere Identifier:
    hdl: 10419/278467
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 677 (April 2023)
    Schlagworte: environmental policy; partial observation; real options; optimal stopping; free boundaries
    Umfang: 1 Online-Ressource (circa 27 Seiten), Illustrationen
  8. Monetary policy and sovereign debt vulnerability
    Erschienen: 2015
    Verlag:  Banco de España, Madrid

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    Schriftenreihe: Documentos de trabajo / Banco de España, Eurosistema ; no. 1517
    Schlagworte: monetary- fiscal interactions; discretion; sovereign default; continuous time; optimal stopping
    Umfang: 1 Online-Ressource (circa 54 Seiten), Illustrationen
    Bemerkung(en):

    Zusammenfassung in spanischer Sprache

  9. What to study and when
    a dynamic Roy model of specialization
    Erschienen: [2023]
    Verlag:  The Foerder Institute for Economic Research, Tel Aviv University, The Eitan Berglas School of Economics, Tel Aviv, Israel

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    Schriftenreihe: Discussion paper / Foerder Institute for Economic Research and the Sackler Institute for Economic Studies ; no. 2023, 8
    Schlagworte: education; human capital; specialization; learning; optimal switching; optimal stopping; dynamic Roy model
    Umfang: 1 Online-Ressource (circa 45 Seiten), Illustrationen
  10. Irreversible reinsurance
    minimization of capital injections in presence of a fixed cost
    Erschienen: [2023]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the insurance... mehr

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    We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the insurance company evolves according to the diffusive approximation of the Cramér-Lundberg model, claims arrive at a fixed constant rate, and the distribution of their sizes is general. Furthermore, we do not specify any specific functional form of the retention level. The aim of the company is to take actions in order to minimize the sum of the expected value of the total discounted flow of capital injections needed to avoid bankruptcy and of the fixed activation cost of the reinsurance contract. We provide an explicit solution to this problem, which involves the resolution of a static nonlinear optimization problem and of an optimal stopping problem for a reflected diffusion. We then illustrate the theoretical results in the case of proportional and excess-of-loss reinsurance, by providing a numerical study of the dependency of the optimal solution with respect to the model's parameters.

     

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    Weitere Identifier:
    hdl: 10419/283395
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 682 (September 2023)
    Schlagworte: reinsurance; fixed cost; capital injections; diffusive risk model; optimal stopping
    Umfang: 1 Online-Ressource (circa 24 Seiten), Illustrationen
  11. Matching workers
    Erschienen: [2024]
    Verlag:  The Foerder Institute for Economic Research, Tel Aviv University, The Eitan Berglas School of Economics, Tel Aviv, Israel

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    Schriftenreihe: Discussion paper / Foerder Institute for Economic Research and the Sackler Institute for Economic Studies ; no. 2024, 1
    Schlagworte: worker interactions; firm value; complementarity; worker value; organizational capital; Salop circle; hiring; hiring; match quality; optimal stopping
    Umfang: 1 Online-Ressource (circa 47 Seiten), Illustrationen
  12. Representable options
    Autor*in: Lenga, Matthias
    Erschienen: 2017

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    Technische Informationsbibliothek (TIB) / Leibniz-Informationszentrum Technik und Naturwissenschaften und Universitätsbibliothek
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    Beteiligt: Kallsen, Jan (AkademischeR BetreuerIn)
    Sprache: Englisch
    Medientyp: Dissertation
    Format: Online
    Weitere Identifier:
    Schlagworte: American options; duality; optimal stopping; optimization methods for option pricing; semi-infinite linear programming
    Umfang: 1 Online-Ressource (circa 137 Seiten), Illustrationen
    Bemerkung(en):

    Dissertation, Christian-Albrechts-Universität zu Kiel, 2017