Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the...Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and CA＇B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and CA＇B copulas show that our method performs better both in computation speed and accuracy.展开更多
Owing to potential regulation capacities from flexible resources in energy coupling,storage,and consumption links,central energy stations(CESs)can provide additional support to power distribution network(PDN)in case o...Owing to potential regulation capacities from flexible resources in energy coupling,storage,and consumption links,central energy stations(CESs)can provide additional support to power distribution network(PDN)in case of power disruption.However,existing research has not explicitly revealed the emergency response of PDN with leveraging multiple CESs.This paper proposes a decentralized self-healing strategy of PDN to minimize the entire load loss,in which multi-area CESs’potentials including thermal storage and building thermal inertia,as well as the flexible topology of PDN,are reasonably exploited for service recovery.For sake of privacy preservation,the co-optimization of PDN and CESs is realized in a decentralized manner using adaptive alternating direction method of multipliers(ADMM).Furtherly,bilateral risk management with conditional value-at-risk(CVaR)for PDN and risk constraints for CESs is integrated to deal with uncertainties from outage duration.Case studies are conducted on a modified IEEE 33-bus PDN with multiple CESs.Numerical results illustrate that the proposed strategy can fully utilize the potentials of multi-area CESs for coordinated load restoration.The effectiveness of the performance and behaviors’adaptation against random risks is also validated.展开更多
Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have marting...Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap（CDS） with bilateral counterparty risk is derived.展开更多
基金supported by the National Natural Science Foundation of China(Grants No.11671021,11271033)National Social Science Fund of China(Grant No.16ZDA052)
文摘Based on the framework of [7], we discuss pricing bilateral counterparty risk of CDS, where each individual default intensity is modeled by a shifted CIR process with jump （3CIR＋＋）, and the correlation between the default times is modeled by a copula function. We present a semi-analytical formula for pricing bilateral counterparty risk of CDS, which is more convenient to compute through calculating multiple numerical integration or using Monte-Carlo simulation without simulating default times. Moreover, we obtain simpler formulae under FGM copulas, Bernstein copulas and CA＇B copulas, which can be applied for speeding up the computation and reducing the pricing error. Numerical results under FGM copulas and CA＇B copulas show that our method performs better both in computation speed and accuracy.
基金financially supported by the Fundamental Research Funds for the Central Universities(No.2021QN1066)。
文摘Owing to potential regulation capacities from flexible resources in energy coupling,storage,and consumption links,central energy stations(CESs)can provide additional support to power distribution network(PDN)in case of power disruption.However,existing research has not explicitly revealed the emergency response of PDN with leveraging multiple CESs.This paper proposes a decentralized self-healing strategy of PDN to minimize the entire load loss,in which multi-area CESs’potentials including thermal storage and building thermal inertia,as well as the flexible topology of PDN,are reasonably exploited for service recovery.For sake of privacy preservation,the co-optimization of PDN and CESs is realized in a decentralized manner using adaptive alternating direction method of multipliers(ADMM).Furtherly,bilateral risk management with conditional value-at-risk(CVaR)for PDN and risk constraints for CESs is integrated to deal with uncertainties from outage duration.Case studies are conducted on a modified IEEE 33-bus PDN with multiple CESs.Numerical results illustrate that the proposed strategy can fully utilize the potentials of multi-area CESs for coordinated load restoration.The effectiveness of the performance and behaviors’adaptation against random risks is also validated.
基金Supported by Jiangsu Government Scholarship for Overseas Studiesthe NNSF of China(Grant Nos.11401419,11301369,11371274)+1 种基金the CPSF(2014M561453)the NSF of Jiangsu Province(Grant Nos.BK20140279,BK20130260)
文摘Regime switching,which is described by a Markov chain,is introduced in a Markov copula model.We prove that the marginals（X,H^i）,i = 1,2,3 of the Markov copula model（X,H） are still Markov processes and have martingale property.In this proposed model,a pricing formula of credit default swap（CDS） with bilateral counterparty risk is derived.
