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A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap 被引量:3
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作者 白云芬 胡新华 叶中行 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第12期1643-1649,共7页
A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner. If two firms are competitors (copartners), the default intensity of one firm will decrease (increase) ab... A hyperbolic function is introduced to reflect the attenuation effect of one firm's default to its partner. If two firms are competitors (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap (CDS) can be valued. 展开更多
关键词 dependent default hyperbolic attenuation function change of measure credit default swap (CDS)
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Model of counterparty risk with geometric attenuation and valuation of CDS
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作者 Bai Yunfen1,2 Hu Xinhua3,4 Ye Zhongxing1(1 Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China)(2 Department of Mathematics, Shijiazhuang College, Shijiazhuang 050035, China)(3 Guanghua Institute of Management, Peking University, Beijing 100032, China)(4 Postdoctoral Workstation of ICBC, Beijing 100036, China) 《Journal of Southeast University(English Edition)》 EI CAS 2008年第S1期196-198,共3页
To investigate the impact of microstructure interdependency of a counterparty explicitly, a geometric function is introduced in one firm's default intensity to reflect the attenuation behavior of the impact of its... To investigate the impact of microstructure interdependency of a counterparty explicitly, a geometric function is introduced in one firm's default intensity to reflect the attenuation behavior of the impact of its counterparty firm's default. The general joint distribution and marginal distributions of default times are derived by employing the change of measure. The fair premium of a vanilla CDS (credit default swap) is obtained in continuous and discrete contexts, respectively. The swap premium in a discrete context is similar to the accumulated interest during the period between two payment days, and the short rate is the swap rate in a continuous context. 展开更多
关键词 counterparty risk dependent default attenuation function change of measure credit default swap
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The Spread Speed of Multiple Catalytic Branching Random Walks
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作者 Rong-li LIU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2023年第2期262-292,共31页
In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk(X_(n))on Z.If M_(n) is its maximal position at time n,we prove that there is a constan... In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk(X_(n))on Z.If M_(n) is its maximal position at time n,we prove that there is a constantα>0 such that M_(n)/n converges toαalmost surely on the set of infinite number of visits to the set of catalysts.We also derive the asymptotic law of the centered process M_(n)-αn as n→∞.Our results are similar to those in[13].However,our results are proved under the assumption of finite L log L moment instead of finite second moment.We also study the limit of(X_(n))as a measure-valued Markov process.For any function f with compact support,we prove a strong law of large numbers for the process X_(n)(f). 展开更多
关键词 catalytic branching random walk invariant measure martingale change of measure spine decomposition
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ANALYSIS OF INCOMPLETE STOCK MARKET WITH JUMP-DIFFUSION UNCERTAINTY
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作者 Xiuli Chao +1 位作者 Indrajit Bardhan 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2002年第4期337-352,共16页
This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-dif... This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-diffusion uncertainty and have random but predictable jumps. The space of risk-neutral measures that are associated with the market is identified and related to fictitious completions. The construction of replicating portfolios is discussed, and convex duality methods are used to prove existence of optimal consumption and investment policies for a problem of utility maximization. 展开更多
关键词 Incomplete market jump-diffusion process point processes stochastic intensity risk-neutral measure change of measure and utility maximization.
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Some Results behind Dividend Problems 被引量:1
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作者 Ming Zhou Li Wei Jun-yi Guo 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2006年第4期681-686,共6页
We consider the basic dividend problem of the compound Poisson model with constant barrier strategy. Some results concealed behind the dividend problem are made explicit in the present work. Different methods and some... We consider the basic dividend problem of the compound Poisson model with constant barrier strategy. Some results concealed behind the dividend problem are made explicit in the present work. Different methods and some of which are firstly given in this paper. All these results presented certain direct relationship between some important actuary variables in classical risk theory is also revealed. 展开更多
关键词 Compound Poisson process discount dividend payments integro-differential equation change of measure shift operator
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A contagion model with Markov regime-switching intensities 被引量:1
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作者 Yinghui DONG Guojing WANG 《Frontiers of Mathematics in China》 SCIE CSCD 2014年第1期45-62,共18页
We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homog... We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of 'change of measure' and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps (CDSs) on two underlyings. 展开更多
关键词 Credit default swap (CDS) contagion model REGIME-SWITCHING change of measure
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On Optimal Proportional Reinsurance and Investment in a Hidden Markov Financial Market
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作者 Qing-bin MENG Xin ZHANG Jun-na BI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第1期53-62,共10页
This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky (bond) and risky (stock) asset. We assume that only the price of the risky asset can be ob... This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky (bond) and risky (stock) asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function. 展开更多
关键词 hidden Markov chain exponential utility Girsanov change of measure dynamic programming.
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