Economics - Research Publications

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Author: Li, Shuanming × End date: 2009 ×

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    The Distribution of the Dividend Payments in theCompound Poisson Risk Model Perturbed byDiffusion
    LI, SHUANMING ( 2005-02)
    We consider a diffusion perturbed classical compound Poisson risk model in the presence of a constant dividend barrier. An integro-differential equation with certain boundary conditions for the n-th moment of the discounted dividend payments prior to ruin is derived and solved. Its solution can be expressed in terms of the expected discounted penalty (Gerber-Shiu) functions due to oscillation in the corresponding perturbed risk model without a barrier. When the discount factor is zero, we show that all the results can be expressed in terms of the non-ruin probability in the perturbed risk model without a barrier.
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    Some Optimal Dividend Problems in aMarkov-modulated Risk Model
    LI, SHUANMING ; LU, YI ( 2006-01)
    In this paper, we derive some results on the dividend payments prior toruin in a Markov-modulated risk model in which the claim inter-arrivals,claim sizes and premiums are influenced by an external Markovian environmentprocess. A system of integro-differential equations with boundaryconditions satisfied by the n-th moment of present value of the total dividendpayments prior to ruin, given the initial environment state, is derivedand solved. We show that both the probabilities that the surplus processattains a given level from the initial surplus without first falling below zeroand the Laplace transforms of the time that the surplus process first hits abarrier without ruin occuring can be expressed in term of the solution of theabove mentioned system of integro-differential equations. In the two-statemodel, explicit solutions to the integro-differential equations are obtainedwhen both claim size distributions are exponentially distributed. Finally, anumerical example and the comparison with the results obtained from theassociated averaged compound Poisson risk model are also given.
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    The Diffusion Perturbed Compound Poisson RiskModel with a Dividend Barrier
    LI, SHUANMING ; Wu, Biao ( 2006-02)
    We consider a diffusion perturbed classical compound Poisson risk modelin the presence of a constant dividend barrier. Integro-differential equationswith certain boundary conditions for the expected discounted penalty(Gerber-Shiu) functions (caused by oscillations or by a claim) are derivedand solved. Their solutions can be expressed in terms of the Gerber-Shiufunctions in the corresponding perturbed risk model without a barrier. Finally,explicit results are given when the claim sizes are rationally distributed.
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    On a discrete time risk model with delayed claimsand a constant dividend barrier
    WU, XUEYUAN ; LI, SHUANMING ( 2006)
    In this paper a compound binomial risk model with a constant dividend barrier isconsidered. Two types of individual claims, main claims and by-claims, are de¯ned,where by-claims are produced by the main claims and may be delayed for one timeperiod with a certain probability. Some prior work on these time-correlated claimshas been done by Yuen and Guo (2001) and the references therein. Formulae for theexpected present value of dividend payments up to the time of ruin are obtained fordiscrete-type individual claims, together with some other results of interest. Explicitexpressions for the corresponding results are derived in a special case, for which acomparison is also made to the original discrete model of De Finetti (1957).