ORCID Profile
0000-0003-4102-4618
Current Organisation
University of Melbourne
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Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 16-05-2022
DOI: 10.1137/21M1422318
Publisher: Cambridge University Press (CUP)
Date: 31-05-2011
DOI: 10.1017/S1748499511000054
Abstract: We consider an insurer who has a fixed amount of funds allocated as the initial surplus for a risk portfolio, so that the probability of ultimate ruin for this portfolio is at a known level. We consider the question of whether the insurer can reduce this ultimate ruin probability by allocating part of the initial funds to the purchase of a reinsurance contract. This reinsurance contract would restore the insurer's surplus to a positive level k every time the surplus fell between 0 and k . The insurer's objective is to choose the level k that minimizes the ultimate ruin probability. Using different ex les of reinsurance premium calculation and claim size distribution we show that this objective can be achieved, often with a substantial reduction in the ultimate ruin probability from the situation when there is no reinsurance. We also show that by purchasing reinsurance the insurer can release funds for other purposes without altering its ultimate ruin probability.
Publisher: Elsevier BV
Date: 02-2021
Publisher: Springer Science and Business Media LLC
Date: 05-03-2013
Publisher: Elsevier BV
Date: 2022
Publisher: Elsevier BV
Date: 08-2009
Publisher: Elsevier BV
Date: 02-2010
Publisher: Elsevier BV
Date: 04-2013
Publisher: Cambridge University Press (CUP)
Date: 05-2005
DOI: 10.1017/S0515036100014069
Abstract: We consider a risk model with two independent classes of insurance risks. We assume that the two independent claim counting processes are, respectively, Poisson and Sparre Andersen processes with generalized Erlang(2) claim inter-arrival times. The Laplace transform of the non-ruin probability is derived from a system of integro-differential equations. Explicit results can be obtained when the initial reserve is zero and the claim severity distributions of both classes belong to the K n family of distributions. A relation between the ruin probability and the distribution of the supremum before ruin is identified. Finally, the Laplace transform of the non-ruin probability of a perturbed Sparre Andersen risk model with generalized Erlang(2) claim inter-arrival times is derived when the compound Poisson process converges weakly to a Wiener process.
Publisher: Informa UK Limited
Date: 04-2007
Publisher: Elsevier BV
Date: 11-2023
Publisher: Cambridge University Press (CUP)
Date: 04-11-2013
DOI: 10.1017/S1748499513000110
Abstract: In this paper, we investigate the density function of the time of ruin in the classical risk model with a constant idend barrier. When claims are exponentially distributed, we derive explicit expressions for the density function of the time of ruin and its decompositions: the density of the time of ruin without idend payments and the density of the time of ruin with idend payments. These densities are obtained based on their Laplace transforms, and expressed in terms of some special functions which are computationally tractable. The Laplace transforms are being inverted using a magnificent tool, the Lagrange inverse formula, developed in Dickson and Willmot (2005). Several numerical ex les are given to illustrate our results.
Publisher: Elsevier BV
Date: 04-2009
Publisher: Elsevier BV
Date: 03-2013
Publisher: Informa UK Limited
Date: 12-2009
Publisher: Elsevier BV
Date: 10-2022
Publisher: Informa UK Limited
Date: 10-2008
Publisher: Elsevier BV
Date: 12-2004
Publisher: Elsevier BV
Date: 05-2015
Publisher: Informa UK Limited
Date: 05-09-2014
Publisher: Informa UK Limited
Date: 07-2005
Publisher: Informa UK Limited
Date: 04-2005
Publisher: Elsevier BV
Date: 2020
Publisher: Informa UK Limited
Date: 04-2005
Publisher: Elsevier BV
Date: 04-2005
Publisher: Elsevier BV
Date: 11-2021
Publisher: Informa UK Limited
Date: 09-2012
Publisher: Informa UK Limited
Date: 04-2008
Publisher: Elsevier BV
Date: 08-2023
Publisher: Cambridge University Press (CUP)
Date: 02-11-2022
DOI: 10.1017/S0269964822000353
Abstract: This paper studies the open-loop equilibrium strategies for a class of non-zero-sum reinsurance–investment stochastic differential games between two insurers with a state-dependent mean expectation in the incomplete market. Both insurers are able to purchase proportional reinsurance contracts and invest their wealth in a risk-free asset and a risky asset whose price is modeled by a general stochastic volatility model. The surplus processes of two insurers are driven by two standard Brownian motions. The objective for each insurer is to find the equilibrium investment and reinsurance strategies to balance the expected return and variance of relative terminal wealth. Incorporating the forward backward stochastic differential equations (FBSDEs), we derive the sufficient conditions and obtain the general solutions of equilibrium controls for two insurers. Furthermore, we apply our theoretical results to two special stochastic volatility models (Hull–White model and Heston model). Numerical ex les are also provided to illustrate our results.
Publisher: Elsevier BV
Date: 05-2009
Publisher: Elsevier BV
Date: 05-2013
Publisher: Springer Science and Business Media LLC
Date: 09-2009
DOI: 10.1007/BF03191910
Publisher: Informa UK Limited
Date: 28-08-2013
Publisher: Informa UK Limited
Date: 30-09-2022
Publisher: Elsevier BV
Date: 12-2017
Publisher: Informa UK Limited
Date: 06-2010
Publisher: Springer Science and Business Media LLC
Date: 05-07-2015
Publisher: Elsevier BV
Date: 02-2010
Publisher: Informa UK Limited
Date: 20-01-2016
Publisher: Informa UK Limited
Date: 05-2005
Publisher: Elsevier BV
Date: 06-2004
Publisher: Informa UK Limited
Date: 03-2006
Publisher: Cambridge University Press (CUP)
Date: 09-2005
Abstract: We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a K n distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n ∈ N ). The Laplace transform of the expected discounted penalty function at ruin is derived. This leads to a generalization of the defective renewal equations given by Willmot (1999) and Gerber and Shiu (2005). Finally, explicit results are given for rationally distributed claim severities.
Publisher: Elsevier BV
Date: 2023
Publisher: Elsevier BV
Date: 11-2016
Publisher: MDPI AG
Date: 23-05-2018
DOI: 10.3390/RISKS6020059
Publisher: Informa UK Limited
Date: 07-2005
Publisher: Elsevier BV
Date: 03-2020
Publisher: Cambridge University Press (CUP)
Date: 13-07-2018
DOI: 10.1017/S1748499518000209
Abstract: This paper starts with the Beta transform and discusses the stochastic ordering properties of this transform under different parameter settings. Later, the distribution of discounted aggregate claims in a compound renewal risk model with dependence between inter-claim times and claim sizes is studied. Recursive formulas for moments and joint moments are expressed in terms of the Beta transform of the inter-claim times and claim severities. Particularly, our moments formula is more explicit and computation-friendly than earlier ones in the references. Lastly, numerical ex les are provided to illustrate our results.
Publisher: Informa UK Limited
Date: 10-2008
Publisher: Elsevier BV
Date: 11-2015
Publisher: Informa UK Limited
Date: 07-2003
Publisher: Elsevier BV
Date: 12-2020
Publisher: Hindawi Limited
Date: 20-10-2020
DOI: 10.1155/2020/5830245
Abstract: In this paper, we study some state-specific one-sided exit probabilities in a Markov-modulated risk process including the probability that ruin occurs without or with the surplus visiting certain states the probability that ruin occurs without or with a claim occurring in certain states the probability that the surplus attains a target level without or with visiting certain states and the probability that the surplus attains a target level without or with a claim occurring in certain states. We also investigate the corresponding two-sided first exit probabilities without (or with) the surplus visiting certain states or without (or with) claims occurring in certain states. All these probabilities can be expressed elegantly in terms of some modified matrix scale functions which are easily computable.
Publisher: Elsevier BV
Date: 06-2006
Publisher: Elsevier BV
Date: 12-2005
Publisher: Informa UK Limited
Date: 07-01-2019
Publisher: Informa UK Limited
Date: 07-2008
Publisher: Elsevier BV
Date: 05-2021
Publisher: Elsevier BV
Date: 11-2016
Publisher: Informa UK Limited
Date: 02-10-2013
No related grants have been discovered for Shuanming Li.