In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly ...In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo(MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index(SSECI) with respect to the proposed SV-dt C model and two classic SV-N(SV model with Normal distribution)and SV-T(SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dt C model has better performance by model checking, including independence test(Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion(DIC) also shows that the proposed model has a significant improvement in model fit over the others.展开更多
An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is...An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.展开更多
The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requireme...The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.展开更多
It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-D...It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.展开更多
A new stochastic volatility(SV)method to estimate the conditional value at risk(CVaR)is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo(MCMC...A new stochastic volatility(SV)method to estimate the conditional value at risk(CVaR)is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo(MCMC)simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk(GARCH-VaR)model.Empirical study suggests that this model is better than GARCH-VaR model in this field.展开更多
Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing Euro...Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing European options,defined in the study by Jerbi(Quantitative Finance,15:2041-2052,2015).The J-am pricing formula is a solution of the Black&Scholes(BS)PDE with an additional function called f as a second member and with limit conditions adapted to the American option context.The aforesaid function f represents the cash flows resulting from an early exercise of the option.Methods:This study develops the theoretical formulas of the early exercise premium value related to three American option pricing models called J-am,BS-am,and Heston-am models.These three models are based on the J-formula by Jerbi(Quantitative Finance,15:2041-2052,2015),BS model,and Heston(Rev Financ Stud,6:327-343,1993)model,respectively.This study performs a general algorithm leading to the EEB and to the American option price for the three models.Results:After implementing the algorithms,we compare the three aforesaid models in terms of pricing and the EEB curve.In particular,we examine the equivalence between J-am and Heston-am as an extension of the equivalence studied by Jerbi(Quantitative Finance,15:2041-2052,2015).This equivalence is interesting since it can reduce a bi-dimensional model to an equivalent uni-dimensional model.Conclusions:We deduce that our model J-am exactly fits the Heston-am one for certain parameters values to be optimized and that all the theoretical results conform with the empirical studies.The required CPU time to compute the solution is significantly less in the case of the J-am model compared with to the Heston-am model.展开更多
This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is ...This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.展开更多
In the stock market, some popular technical analysis indicators (e.g. Bollinger Bands, RSI, ROC, ...) are widely used by traders. They use the daily (hourly, weekly, ...) stock prices as samples of certain statist...In the stock market, some popular technical analysis indicators (e.g. Bollinger Bands, RSI, ROC, ...) are widely used by traders. They use the daily (hourly, weekly, ...) stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes' stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.展开更多
Increasing attention has been focused on the analysis of the realized volatil- ity, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a pr...Increasing attention has been focused on the analysis of the realized volatil- ity, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.展开更多
This study investigates the basic numeric characteristics of Chinese A-share market index volatility (i.e.,the clustering,heteroscedasticity,and jumps) from the perspective of data mining.It presents a theoretical-emp...This study investigates the basic numeric characteristics of Chinese A-share market index volatility (i.e.,the clustering,heteroscedasticity,and jumps) from the perspective of data mining.It presents a theoretical-empirical model based on these three major characteristics and conducts a maximum likelihood estimation to study Chinese A-share market return data empirically.Results show that,in full-sample or special periods,this model calibrates the A-share index volatility well and simulates in-sample volatility better than the four major empirical models adopted to study volatility.In out-of-sample forecasts,this model performs better than the other four models on the value-at-risk dates,which are the volatile days.This model can also decompose and explain the volatility of the Chinese A-share index.On the basis of GARCH,this study revises the volatility model proposed by Maheu and extends Engle’s research framework.Thus,this model is of theoretical significance.This model’s simulation and forecast functioning can contribute to regulatory expectation management and investment portfolio construction.展开更多
A factor separation technique and an improved regional air quality model (RAQM) were applied to calculate synergistic contributions of anthropogenic volatile organic compounds (AVOCs),biogenic volatile organic com...A factor separation technique and an improved regional air quality model (RAQM) were applied to calculate synergistic contributions of anthropogenic volatile organic compounds (AVOCs),biogenic volatile organic compounds (BVOCs) and nitrogen oxides (NOx) to daily maximum surface O3(O3DM) concentrations in East Asia in summer (June to August 2000).The summer averaged synergistic impacts of AVOCs and NOx are dominant in most areas of North China,with a maximum of 60 ppbv,while those of BVOCs and NOx are notable only in some limited areas with high BVOC emissions in South China,with a maximum of 25 ppbv.This result implies that BVOCs contribute much less to summer averaged O3DM concentrations than AVOCs in most areas of East Asia at a coarse spatial resolution (1×1) although global emissions of BVOCs are much greater than those of AVOCs.Daily maximum total contributions of BVOCs can approach 20 ppbv in North China,but they can reach 40 ppbv in South China,approaching or exceeding those in some developed countries in Europe and North America.BVOC emissions in such special areas should be considered when O3 control measures are taken.Synergistic contributions among AVOCs,BVOCs and NOx significantly enhance O3 concentrations in the Beijing-Tianjin-Tangshan region and decrease them in some areas in South China.Thus,the total contributions of BVOCs to O3DM vary significantly from day to day and from location to location.This result suggests that O3 control measures obtained from episodic studies could be limited for long-term applications.展开更多
In this paper, we study the GJR scaling model which embeds the intraday return processes into the daily GJR model and propose a class of robust M-estimates for it. The estimation procedures would be more efficient whe...In this paper, we study the GJR scaling model which embeds the intraday return processes into the daily GJR model and propose a class of robust M-estimates for it. The estimation procedures would be more efficient when high-frequency data is taken into the model. However, high-frequency data brings noises and outliers which may lead to big bias of the estimators. Therefore, robust estimates should be taken into consideration. Asymptotic results are derived from the robust M-estimates without the finite fourth moment of the innovations. A simulation study is carried out to assess the performance of the model and its estimates.Robust M-estimate of GJR model is also applied in predicting Va R for real financial time series.展开更多
In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsuran...In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.展开更多
Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several...Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several simulation results are presented to demonstrate the e ectiveness;several applications of the 2BSDEs are investigated.It is concluded from these results that the proposed the method is powerful to calculate the 2BSDEs listing from the nancial engineering.展开更多
基金supported by the Open Fund of State Key Laboratory of New Metal Materials,Beijing University of Science and Technology (No.2022Z-18)。
文摘In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dt C model, a stochastic volatility(SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo(MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index(SSECI) with respect to the proposed SV-dt C model and two classic SV-N(SV model with Normal distribution)and SV-T(SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dt C model has better performance by model checking, including independence test(Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion(DIC) also shows that the proposed model has a significant improvement in model fit over the others.
基金National Natural Science Foundation of China(No.62073071)Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University,China(No.CUSF-DH-D-2021045)。
文摘An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.
文摘The main business of Life Insurers is Long Term contractual obligations with a typical lifetime of 20 - 40 years. Therefore, the Solvency metric is defined by the adequacy of capital to service the cash flow requirements arising from the said obligations. The main component inducing volatility in Capital is market sensitive Assets, such as Bonds and Equity. Bond and Equity prices in Sri Lanka are highly sensitive to macro-economic elements such as investor sentiment, political stability, policy environment, economic growth, fiscal stimulus, utility environment and in the case of Equity, societal sentiment on certain companies and industries. Therefore, if an entity is to accurately forecast the impact on solvency through asset valuation, the impact of macro-economic variables on asset pricing must be modelled mathematically. This paper explores mathematical, actuarial and statistical concepts such as Brownian motion, Markov Processes, Derivation and Integration as well as Probability theorems such as the Probability Density Function in determining the optimum mathematical model which depicts the accurate relationship between macro-economic variables and asset pricing.
基金National Natural Science Foundation of China(No.71401144)
文摘It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.
基金Sponsored by the National Natural Science Foundation of China(70571010)
文摘A new stochastic volatility(SV)method to estimate the conditional value at risk(CVaR)is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo(MCMC)simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk(GARCH-VaR)model.Empirical study suggests that this model is better than GARCH-VaR model in this field.
文摘Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing European options,defined in the study by Jerbi(Quantitative Finance,15:2041-2052,2015).The J-am pricing formula is a solution of the Black&Scholes(BS)PDE with an additional function called f as a second member and with limit conditions adapted to the American option context.The aforesaid function f represents the cash flows resulting from an early exercise of the option.Methods:This study develops the theoretical formulas of the early exercise premium value related to three American option pricing models called J-am,BS-am,and Heston-am models.These three models are based on the J-formula by Jerbi(Quantitative Finance,15:2041-2052,2015),BS model,and Heston(Rev Financ Stud,6:327-343,1993)model,respectively.This study performs a general algorithm leading to the EEB and to the American option price for the three models.Results:After implementing the algorithms,we compare the three aforesaid models in terms of pricing and the EEB curve.In particular,we examine the equivalence between J-am and Heston-am as an extension of the equivalence studied by Jerbi(Quantitative Finance,15:2041-2052,2015).This equivalence is interesting since it can reduce a bi-dimensional model to an equivalent uni-dimensional model.Conclusions:We deduce that our model J-am exactly fits the Heston-am one for certain parameters values to be optimized and that all the theoretical results conform with the empirical studies.The required CPU time to compute the solution is significantly less in the case of the J-am model compared with to the Heston-am model.
基金isupported by the National Natural Science Foundation of China(Grant Nos.11871010 and 11971040)the Fundamental Research Funds for the Central Universities(Grant No.2019XD-A11)The work of Weilin Xiao is supported by the Humanities and Social Sciences of Ministry of Education Planning Fund of China(Grant No.23YJA630102).
文摘This study considers an optimal investment and reinsurance problem involving a defaultable security for an insurer in an ambiguous environment.In other words,the insurer is ambiguous about the insurance claim that is exponentially distributed with an uncertain rate parameter.The insurer can purchase proportional reinsurance and invest its wealth in three assets:a risk-free asset,a risky asset,the price process of which satisfies the Heston local-stochastic volatility model,and a defaultable corporate bond.For the optimal investment–reinsurance objective with a smooth ambiguity utility proposed by Klibanoff,P.,Marinacci,M.,and Mukerji,S.[A smooth model of decision making under ambiguity,Econometrica,2005,73(6):1849-1892],the equilibrium strategy is introduced and the extended Hamilton–Jacobi–Bellman equation is established through a stochastic control approach.However,the analytical solution of the strategy under the Heston local-stochastic volatility model cannot be obtained because of the complicated nonlinearity of the partial differential equation.In this study,we employ a perturbation method to derive an asymptotic solution for the post-and pre-default cases.In addition,we present a sensitivity analysis to explain the impact of model parameters on the equilibrium investment–reinsurance strategy.
基金Partially supported by National Natural Science Foundation of China (Grant No. 10971068), National Basic Research Program of China (973 Program) (Grant No. 2007CB814904) and Key Subject Construction Project of Shanghai Education Commission (Grant No. J51601)
文摘In the stock market, some popular technical analysis indicators (e.g. Bollinger Bands, RSI, ROC, ...) are widely used by traders. They use the daily (hourly, weekly, ...) stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-known indicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes' stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.
文摘Increasing attention has been focused on the analysis of the realized volatil- ity, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.
基金sponsored by the project “Investor Sentiment, Behavior, Environmental Constraints and Excess Volatility of China Stock Market:A Particular Practice from China and the Study of General Theory”(No. 71673226) of the National Natural Science Foundation of China。
文摘This study investigates the basic numeric characteristics of Chinese A-share market index volatility (i.e.,the clustering,heteroscedasticity,and jumps) from the perspective of data mining.It presents a theoretical-empirical model based on these three major characteristics and conducts a maximum likelihood estimation to study Chinese A-share market return data empirically.Results show that,in full-sample or special periods,this model calibrates the A-share index volatility well and simulates in-sample volatility better than the four major empirical models adopted to study volatility.In out-of-sample forecasts,this model performs better than the other four models on the value-at-risk dates,which are the volatile days.This model can also decompose and explain the volatility of the Chinese A-share index.On the basis of GARCH,this study revises the volatility model proposed by Maheu and extends Engle’s research framework.Thus,this model is of theoretical significance.This model’s simulation and forecast functioning can contribute to regulatory expectation management and investment portfolio construction.
基金supported by the National Natural Science Foundation of China(No.40905055,41175105)the Key Project of the Chinese Academy of Sciences(No.KZCX1-YW-06-04)
文摘A factor separation technique and an improved regional air quality model (RAQM) were applied to calculate synergistic contributions of anthropogenic volatile organic compounds (AVOCs),biogenic volatile organic compounds (BVOCs) and nitrogen oxides (NOx) to daily maximum surface O3(O3DM) concentrations in East Asia in summer (June to August 2000).The summer averaged synergistic impacts of AVOCs and NOx are dominant in most areas of North China,with a maximum of 60 ppbv,while those of BVOCs and NOx are notable only in some limited areas with high BVOC emissions in South China,with a maximum of 25 ppbv.This result implies that BVOCs contribute much less to summer averaged O3DM concentrations than AVOCs in most areas of East Asia at a coarse spatial resolution (1×1) although global emissions of BVOCs are much greater than those of AVOCs.Daily maximum total contributions of BVOCs can approach 20 ppbv in North China,but they can reach 40 ppbv in South China,approaching or exceeding those in some developed countries in Europe and North America.BVOC emissions in such special areas should be considered when O3 control measures are taken.Synergistic contributions among AVOCs,BVOCs and NOx significantly enhance O3 concentrations in the Beijing-Tianjin-Tangshan region and decrease them in some areas in South China.Thus,the total contributions of BVOCs to O3DM vary significantly from day to day and from location to location.This result suggests that O3 control measures obtained from episodic studies could be limited for long-term applications.
基金Supported by National Natural Science Foundation of China(Grant No.71003100)the Research Funds of Renmin University of China(No.11XNK027)
文摘In this paper, we study the GJR scaling model which embeds the intraday return processes into the daily GJR model and propose a class of robust M-estimates for it. The estimation procedures would be more efficient when high-frequency data is taken into the model. However, high-frequency data brings noises and outliers which may lead to big bias of the estimators. Therefore, robust estimates should be taken into consideration. Asymptotic results are derived from the robust M-estimates without the finite fourth moment of the innovations. A simulation study is carried out to assess the performance of the model and its estimates.Robust M-estimate of GJR model is also applied in predicting Va R for real financial time series.
基金This research was supported by the National Natural Science Foundation of China(No.71801186)the Science Foundation of Ministry of Education of China(No.18YJC630001)the Natural Science Foundation of Guangdong Province of China(No.2017A030310660).
文摘In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.
文摘Schwarz method is put forward to solve second order backward stochastic di erential equations(2BSDEs)in this work.We will analyze uniqueness,convergence,stability and optimality of the proposed method.Moreover,several simulation results are presented to demonstrate the e ectiveness;several applications of the 2BSDEs are investigated.It is concluded from these results that the proposed the method is powerful to calculate the 2BSDEs listing from the nancial engineering.