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Cheng-shang Chang - One of the best experts on this subject based on the ideXlab platform.

  • Computable Exponential Bounds for llntree Networks with Routing
    2015
    Co-Authors: Cheng-shang Chang, Jay Cheng, National Tsing, Hua Tjniversity
    Abstract:

    In this paper, we refine the calculus proposed in [5, 8, 91. The new calculus, including network opera-tions for multiplexing, input-output relation, and rout-ing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external ar-rival processes and routing processes are either Markov arrival processes or autoregressive processes, the sta-tionary queue length at a local node is stochastically bounded above b y the sum of a constant and an Er-lang Random Variable. The decay rate of the Erlang Random Variable is not greater than ( in some cases equal to) the decay rate of the tail distribution of the stationa y queue length. The number of stages of th

  • Computable exponential bounds for intree networks with routing
    Institute of Electrical and Electronics Engineers, 2012
    Co-Authors: Cheng-shang Chang
    Abstract:

    [[abstract]]n this paper, we refine the calculus proposed previously by Chang et al. (1994). The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above by the sum of a constant and an Erlang Random Variable. The decay rate of the Erlang Random Variable is not greater than (in some cases equal to) the decay rate of the tail distribution of the stationary queue length. The number of stages of the Erlang Random Variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper-bounds are derived.[[fileno]]2030115030021[[department]]電機工程學

  • Computable Exponential Bounds for Intree Networks with Routing
    1995
    Co-Authors: Cheng-shang Chang, Jay Cheng
    Abstract:

    In this paper, we re ne the calculus proposed in [5, 8, 9]. The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above by the sum of a constant and an Erlang Random Variable. The decay rate of the Erlang Random Variable is not greater than ( in some cases equal to) the decay rate of the tail distribution of the stationary queue length. The number of stages of the Erlang Random Variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper bounds are derived

  • INFOCOM - Computable exponential bounds for intree networks with routing
    Proceedings of INFOCOM'95, 1
    Co-Authors: Cheng-shang Chang, Jay Cheng
    Abstract:

    In this paper, we refine the calculus proposed previously by Chang et al. (1994). The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above by the sum of a constant and an Erlang Random Variable. The decay rate of the Erlang Random Variable is not greater than (in some cases equal to) the decay rate of the tail distribution of the stationary queue length. The number of stages of the Erlang Random Variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper-bounds are derived.

Eric C.k. Cheung - One of the best experts on this subject based on the ideXlab platform.

  • A note on a Lévy insurance risk model under periodic dividend decisions
    Journal of Industrial & Management Optimization, 2018
    Co-Authors: Zhimin Zhang, Eric C.k. Cheung
    Abstract:

    In this paper, we consider a spectrally negative Levy insurance risk process with a barrier-type dividend strategy. In contrast to the traditional barrier strategy in which dividends are payable to the shareholders immediately when the surplus process reaches a fixed level b (as long as ruin has not yet occurred), it is assumed that the insurer only makes dividend decisions at some discrete time points in the spirit of [ 1 ]. Under such a dividend strategy with Erlang inter-dividend-decision times, expressions for the Gerber-Shiu expected discounted penalty function proposed in [ 24 ] and the moments of total discounted dividends payable until ruin are derived. The results are expressed in terms of the scale functions of a spectrally negative Levy process and an embedded spectrally negative Markov additive process. Our analyses rely on the introduction of a potential measure associated with an Erlang Random Variable. Numerical illustrations are also given.

  • ON THE COMPOUND POISSON RISK MODEL WITH PERIODIC CAPITAL INJECTIONS
    ASTIN Bulletin, 2017
    Co-Authors: Zhimin Zhang, Eric C.k. Cheung, Hailiang Yang
    Abstract:

    The analysis of capital injection strategy in the literature of insurance risk models (e.g. Pafumi, 1998; Dickson and Waters, 2004) typically assumes that whenever the surplus becomes negative, the amount of shortfall is injected so that the company can continue its business forever. Recently, Nie et al. (2011) has proposed an alternative model in which capital is immediately injected to restore the surplus level to a positive level b when the surplus falls between zero and b, and the insurer is still subject to a positive ruin probability. Inspired by the idea of Randomized observations in Albrecher et al. (2011b), in this paper, we further generalize Nie et al. (2011)'s model by assuming that capital injections are only allowed at a sequence of time points with inter-capital-injection times being Erlang distributed (so that deterministic time intervals can be approximated using the Erlangization technique in Asmussen et al. (2002)). When the claim amount is distributed as a combination of exponentials, explicit formulas for the Gerber–Shiu expected discounted penalty function (Gerber and Shiu, 1998) and the expected total discounted cost of capital injections before ruin are obtained. The derivations rely on a resolvent density associated with an Erlang Random Variable, which is shown to admit an explicit expression that is of independent interest as well. We shall provide numerical examples, including an application in pricing a perpetual reinsurance contract that makes the capital injections and demonstration of how to minimize the ruin probability via reinsurance. Minimization of the expected discounted capital injections plus a penalty applied at ruin with respect to the frequency of injections and the critical level b will also be illustrated numerically.

  • On the dual risk model with Parisian implementation delays in dividend payments
    European Journal of Operational Research, 2017
    Co-Authors: Eric C.k. Cheung, Jeff T.y. Wong
    Abstract:

    In this paper, we study the dual compound Poisson risk process, which is suitable for a business that pays expenses at a constant rate over time and earns Random amount of income at Random times. In contrast to the usual dividend barrier strategy (e.g. Avanzi, Gerber, and Shiu (2007)) in which any overshoot over a pre-specified barrier is paid immediately to the company’s shareholders as a dividend, it is assumed that dividend is payable only when the process has stayed above the barrier continuously for a certain amount of time d (known as the ‘Parisian implementation delay’ in Dassios and Wu (2009)). Under such a modification, the Laplace transform of the time of ruin and the expected discounted dividends paid until ruin are derived. Motivated by the ‘Erlangization’ technique (e.g. Asmussen, Avram, and Usabel (2002)) of approximating a fixed time using an Erlang distribution, we also analyze the case where the delay d is replaced by an Erlang Random Variable. Numerical illustrations are given to study the effect of Parisian implementation delays on ruin-related quantities and to demonstrate the good performance of Erlangization. Interestingly, unlike the traditional barrier strategy, it is found that the optimal dividend barrier maximizing the expected discounted dividends does depend on the initial surplus level.

Jay Cheng - One of the best experts on this subject based on the ideXlab platform.

  • Computable Exponential Bounds for llntree Networks with Routing
    2015
    Co-Authors: Cheng-shang Chang, Jay Cheng, National Tsing, Hua Tjniversity
    Abstract:

    In this paper, we refine the calculus proposed in [5, 8, 91. The new calculus, including network opera-tions for multiplexing, input-output relation, and rout-ing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external ar-rival processes and routing processes are either Markov arrival processes or autoregressive processes, the sta-tionary queue length at a local node is stochastically bounded above b y the sum of a constant and an Er-lang Random Variable. The decay rate of the Erlang Random Variable is not greater than ( in some cases equal to) the decay rate of the tail distribution of the stationa y queue length. The number of stages of th

  • Computable Exponential Bounds for Intree Networks with Routing
    1995
    Co-Authors: Cheng-shang Chang, Jay Cheng
    Abstract:

    In this paper, we re ne the calculus proposed in [5, 8, 9]. The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above by the sum of a constant and an Erlang Random Variable. The decay rate of the Erlang Random Variable is not greater than ( in some cases equal to) the decay rate of the tail distribution of the stationary queue length. The number of stages of the Erlang Random Variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper bounds are derived

  • INFOCOM - Computable exponential bounds for intree networks with routing
    Proceedings of INFOCOM'95, 1
    Co-Authors: Cheng-shang Chang, Jay Cheng
    Abstract:

    In this paper, we refine the calculus proposed previously by Chang et al. (1994). The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above by the sum of a constant and an Erlang Random Variable. The decay rate of the Erlang Random Variable is not greater than (in some cases equal to) the decay rate of the tail distribution of the stationary queue length. The number of stages of the Erlang Random Variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper-bounds are derived.

Zhimin Zhang - One of the best experts on this subject based on the ideXlab platform.

  • A note on a Lévy insurance risk model under periodic dividend decisions
    Journal of Industrial & Management Optimization, 2018
    Co-Authors: Zhimin Zhang, Eric C.k. Cheung
    Abstract:

    In this paper, we consider a spectrally negative Levy insurance risk process with a barrier-type dividend strategy. In contrast to the traditional barrier strategy in which dividends are payable to the shareholders immediately when the surplus process reaches a fixed level b (as long as ruin has not yet occurred), it is assumed that the insurer only makes dividend decisions at some discrete time points in the spirit of [ 1 ]. Under such a dividend strategy with Erlang inter-dividend-decision times, expressions for the Gerber-Shiu expected discounted penalty function proposed in [ 24 ] and the moments of total discounted dividends payable until ruin are derived. The results are expressed in terms of the scale functions of a spectrally negative Levy process and an embedded spectrally negative Markov additive process. Our analyses rely on the introduction of a potential measure associated with an Erlang Random Variable. Numerical illustrations are also given.

  • ON THE COMPOUND POISSON RISK MODEL WITH PERIODIC CAPITAL INJECTIONS
    ASTIN Bulletin, 2017
    Co-Authors: Zhimin Zhang, Eric C.k. Cheung, Hailiang Yang
    Abstract:

    The analysis of capital injection strategy in the literature of insurance risk models (e.g. Pafumi, 1998; Dickson and Waters, 2004) typically assumes that whenever the surplus becomes negative, the amount of shortfall is injected so that the company can continue its business forever. Recently, Nie et al. (2011) has proposed an alternative model in which capital is immediately injected to restore the surplus level to a positive level b when the surplus falls between zero and b, and the insurer is still subject to a positive ruin probability. Inspired by the idea of Randomized observations in Albrecher et al. (2011b), in this paper, we further generalize Nie et al. (2011)'s model by assuming that capital injections are only allowed at a sequence of time points with inter-capital-injection times being Erlang distributed (so that deterministic time intervals can be approximated using the Erlangization technique in Asmussen et al. (2002)). When the claim amount is distributed as a combination of exponentials, explicit formulas for the Gerber–Shiu expected discounted penalty function (Gerber and Shiu, 1998) and the expected total discounted cost of capital injections before ruin are obtained. The derivations rely on a resolvent density associated with an Erlang Random Variable, which is shown to admit an explicit expression that is of independent interest as well. We shall provide numerical examples, including an application in pricing a perpetual reinsurance contract that makes the capital injections and demonstration of how to minimize the ruin probability via reinsurance. Minimization of the expected discounted capital injections plus a penalty applied at ruin with respect to the frequency of injections and the critical level b will also be illustrated numerically.

Cheung Eck - One of the best experts on this subject based on the ideXlab platform.

  • A note on a Lévy insurance risk model under periodic dividend decisions
    'American Institute of Mathematical Sciences (AIMS)', 2018
    Co-Authors: Zhang Z, Cheung Eck
    Abstract:

    © 2017 American Institute of Mathematical Sciences. In this paper, we consider a spectrally negative Lévy insurance risk process with a barrier-type dividend strategy. In contrast to the traditional barrier strategy in which dividends are payable to the shareholders immediately when the surplus process reaches a fixed level b (as long as ruin has not yet occurred), it is assumed that the insurer only makes dividend decisions at some discrete time points in the spirit of [1]. Under such a dividend strategy with Erlang inter-dividend-decision times, expressions for the Gerber-Shiu expected discounted penalty function proposed in [24] and the moments of total discounted dividends payable until ruin are derived. The results are expressed in terms of the scale functions of a spectrally negative Lévy process and an embedded spectrally negative Markov additive process. Our analyses rely on the introduction of a potential measure associated with an Erlang Random Variable. Numerical illustrations are also given