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  1. Optimal surplus-dependent reinsurance under regime-switching in a Brownian risk model
    Autor*in: Eisenberg, Julia; Fabrykowski, Lukas; Schmeck, Maren Diane
    Erschienen: [2021]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company's surplus process is assumed to follow a... mehr

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    Standort:
    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    Signatur:
    DS 263
    Fernleihe:
    keine Fernleihe

     

    In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company's surplus process is assumed to follow a Brownian motion with drift, and the reinsurance price is modelled by a continuoustime Markov chain with two states. The presence of regime-switching complicates substantially the optimal reinsurance problem, as the surplus-independent strategies turn out to be suboptimal. We develop a recursive approach that allows to represent a solution to the corresponding Hamilton-Jacobi-Bellman equation and the corresponding reinsurance strategy as the unique limits of the sequence of solutions to ordinary differential equations and their first and second order derivatives. Via Ito's formula we prove the constructed function to be the value function. Two examples illustrate the recursive procedure along with a numerical approach yielding the direct solution to the HJB equation.

     
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    Quelle: Verbundkataloge
    Sprache: Englisch
    Medientyp: Buch (Monographie)
    Format: Online
    Weitere Identifier:
    hdl: 10419/238126
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 648 (March 2021)
    Schlagworte: Reinsurance; Regime-switching; Brownian motion; Markov chain; Optimal control; HJB equation; Ordinary differential equations; Boundary value problem
    Umfang: 1 Online-Ressource (circa 36 Seiten), Illustrationen
  2. Optimal dividends under Markov-Modulated Bankruptcy Level
    Autor*in: Ferrari, Giorgio; Schuhmann, Patrick; Zhu, Shihao
    Erschienen: [2021]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    This paper proposes and solves an optimal dividend problem in which a two-state regimeswitching environment affects the dynamics of the company's cash surplus and, as a novel feature, also the bankruptcy level. The aim is to maximize the total... mehr

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    Standort:
    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    Signatur:
    DS 263
    Fernleihe:
    keine Fernleihe

     

    This paper proposes and solves an optimal dividend problem in which a two-state regimeswitching environment affects the dynamics of the company's cash surplus and, as a novel feature, also the bankruptcy level. The aim is to maximize the total expected profits from dividends until bankruptcy. The company's optimal dividend payout is therefore influenced by four factors simultaneously: Brownian fluctuations in the cash surplus, as well as regime changes in drift, volatility and bankruptcy levels. In particular, the average profitability can assume different signs in the two regimes. We find a rich structure of the optimal strategy, which, depending on the interaction of the model's parameters, is either of barrier-type or of liquidation-barrier type. Furthermore, we provide explicit expressions of the optimal policies and value functions. Finally, we complement our theoretical results by a detailed numerical study, where also a thorough analysis of the sensitivities of the optimal dividend policy with respect to the problem's parameters is performed.

     
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    Quelle: Verbundkataloge
    Sprache: Englisch
    Medientyp: Buch (Monographie)
    Format: Online
    Weitere Identifier:
    hdl: 10419/249880
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 657 (November 2021)
    Schlagworte: Optimal dividend policy; Regime-switching; Regime-dependent bankruptcy levels; HJB equation; Singular stochastic control
    Umfang: 1 Online-Ressource (circa 35 Seiten), Illustrationen
  3. Solving penalised American options for jump diffusions using the POST algorithm
    Autor*in: Hessing, Jean-Claude; Lange, Rutger-Jan; Ralph, Daniel
    Erschienen: [2022]
    Verlag:  Tinbergen Institute, Amsterdam, The Netherlands

    This article establishes the Poisson optional stopping times (POST) method by [22] as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    Signatur:
    DS 432
    Fernleihe:
    keine Fernleihe

     

    This article establishes the Poisson optional stopping times (POST) method by [22] as a near-universal method for solving liquidity-constrained American options, or, equivalently, penalised optimal-stopping problems. In this setup, the decision maker is permitted to "stop", i.e. exercise the option, only at a set of Poisson arrival times; this can be viewed as a liquidity constraint or "penalty" that limits access to optionality. We use monotonicity arguments in function space to establish that the POST algorithm either (i) finds the solution or (ii) demonstrates that no solution exists. The monotonicity of POST carries over to the discretised setting, where we additionally show geometric convergence and provide convergence bounds. For jump-diffusion processes, dense matrix factorisation may be avoided by using a suitable operator-splitting method for which we prove convergence. We also highlight a connection with linear complementarity problems (LCPs). We use the POST algorithm to value American options and compute early-exercise boundaries for Kou's jump-diffusion model [20] and Heston's stochastic volatility model [14], illustrating the breadth of application and numerical reliability of the method.

     
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    Quelle: Verbundkataloge
    Sprache: Englisch
    Medientyp: Buch (Monographie)
    Format: Online
    Weitere Identifier:
    hdl: 10419/263927
    Schriftenreihe: Array ; TI 2022, 007
    Schlagworte: Optimal stopping; Penalty method; HJB equation; Contraction; Fixed Point; Operator Splitting; Implicit Explicit; Linear Complementarity Problem
    Umfang: 1 Online-Ressource (circa 27 Seiten), Illustrationen
  4. Strategic interactions and uncertainty in decisions to curb greenhouse gas emissions
    Autor*in: Insley, Margaret; Snoddon, Tracy R.; Forsyth, Peter
    Erschienen: June 1, 2018
    Verlag:  Department of Economics, University of Waterloo, Waterloo, Ontario

    Standort:
    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
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    Hinweise zum Inhalt
    Volltext (kostenfrei)
    Quelle: Verbundkataloge
    Sprache: Englisch
    Medientyp: Buch (Monographie)
    Format: Online
    Auflage/Ausgabe: This version: June 1, 2018
    Schriftenreihe: [Waterloo economic series ; # 18, 005]
    Schlagworte: climate change; differential Stackelberg game; uncertainty; HJB equation
    Umfang: 1 Online-Ressource (circa 47 Seiten), Illustrationen