In this paper the insurer＇s solvency ratio model with or without jump diffusion process in the presence of financial distress cost is constructed, where an insurer＇s solvency ratio is characterized by a Markov-modul...In this paper the insurer＇s solvency ratio model with or without jump diffusion process in the presence of financial distress cost is constructed, where an insurer＇s solvency ratio is characterized by a Markov-modulated dynamics. By Girsanov＇s theorem and the option pricing formula, the expected present value of shareholders＇ terminal payoff is provided.展开更多
This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the...This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.展开更多
In this paper, we consider the dividend problem in a two-state Markov-modulated dual risk model, in which the gain arrivals, gain sizes and expenses are influenced by a Markov process. A system of integro-differential...In this paper, we consider the dividend problem in a two-state Markov-modulated dual risk model, in which the gain arrivals, gain sizes and expenses are influenced by a Markov process. A system of integro-differential equations for the expected value of the discounted dividends until ruin is derived. In the case of exponential gain sizes, the equations are solved and the best barrier is obtained via numerical example. Finally, using numerical example, we compare the best barrier and the expected discounted dividends in the two-state Markov-modulated dual risk model with those in an associated averaged compound Poisson risk model. Numerical results suggest that one could use the results of the associated averaged compound Poisson risk model to approximate those for the two-state Markov-modulated dual risk model.展开更多
This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of t...This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of the stock are modulated by a continuous-time stationary Markov chain with finite state. By a pure probabilistic method, the upper bound for the finite-time ruin probability is obtained.展开更多
A queueing model of the Markov-modulated Poisson process (MMPP) with thresholds was investigated. The customer arrival with various arrival rates in the model was viewed as the MMPP. In contrast to the Poisson, s arri...A queueing model of the Markov-modulated Poisson process (MMPP) with thresholds was investigated. The customer arrival with various arrival rates in the model was viewed as the MMPP. In contrast to the Poisson, s arrival process, the MMPP can better describe the situation that the arrival rate changes with changing conditions;therefore, the model fits better with reality. The threshold conversion was added to the model based on the general MMPP/M/C model. When the number of customers in the system exceeds a threshold, all servers work to serve;when the number of customers in the system is less than another threshold, some servers are shut down. This is the congestion-based staffing policy with two thresholds. Specifically, the problems in the slab stocking stage of slab production at the Iron and Steel Complex in China were analysed. In the slab production process, because the rate of the upstream steelmaking is not constant, the rate of slab reaching the slab yard is uncertain. The crane service is used to store slabs in a warehouse. Because the slab arrival rate varies, different numbers of cranes in service need to be optimized for cost control. Thus, MMPP was used to describe slab arrival with varied arrival rates. Therefore, an MMPP/M/C queue with thresholds was used to analyse and solve the practical problems, and the optimal number of service cranes was obtained to minimize the cost of slab stocking.展开更多
The paper presents a new leaky--bucket (LB) model with Markov chain pattern of token generation and traffic arrival. The performance of the new LB model is analyzed in ATM networks. Finally, some results and useful co...The paper presents a new leaky--bucket (LB) model with Markov chain pattern of token generation and traffic arrival. The performance of the new LB model is analyzed in ATM networks. Finally, some results and useful conclusions are given.展开更多
A pricing model for a corporate bond with rating migration risk is established in this article. With the technology of utility-indifference valuation under the Markov-modulated framework, we analyze the price of a mul...A pricing model for a corporate bond with rating migration risk is established in this article. With the technology of utility-indifference valuation under the Markov-modulated framework, we analyze the price of a multi-rating bond and obtain closed formulae in a three-rating case. Based on the pricing formulae, the impacts of the parameters on the indifference price are analyzed and some reasonable financial explanations are provided as well.展开更多
基金Supported by National Natural Science Foundation of China (10671182)Anhui Natural Science Foundation (090416225)+1 种基金Anhui Natural Science Foundation of Universities (KJ2010A037, KJ2010B026)Anhui Natural Science Foundation (10040606Q03)
文摘In this paper the insurer＇s solvency ratio model with or without jump diffusion process in the presence of financial distress cost is constructed, where an insurer＇s solvency ratio is characterized by a Markov-modulated dynamics. By Girsanov＇s theorem and the option pricing formula, the expected present value of shareholders＇ terminal payoff is provided.
文摘This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.
基金Supported in part by the National Natural Science Foundation of China (No. 10971157) and the Ministry of Education of China
文摘In this paper, we consider the dividend problem in a two-state Markov-modulated dual risk model, in which the gain arrivals, gain sizes and expenses are influenced by a Markov process. A system of integro-differential equations for the expected value of the discounted dividends until ruin is derived. In the case of exponential gain sizes, the equations are solved and the best barrier is obtained via numerical example. Finally, using numerical example, we compare the best barrier and the expected discounted dividends in the two-state Markov-modulated dual risk model with those in an associated averaged compound Poisson risk model. Numerical results suggest that one could use the results of the associated averaged compound Poisson risk model to approximate those for the two-state Markov-modulated dual risk model.
文摘This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of the stock are modulated by a continuous-time stationary Markov chain with finite state. By a pure probabilistic method, the upper bound for the finite-time ruin probability is obtained.
基金We thank the referees and editors, whose comments significantly helped the presentation and analysis in this paperThis work is supported by the National Key Research and Development Program of China (2016YFB0901900)+2 种基金the Fund for Innovative Research Groups of the National Natural Science Foundation of China (71621061)the Major International Joint Research Project of the National Natural Science Foundation of China (71520107004)the Major Program of National Natural Science Foundation of China (71790614) and the 111 Project (Bl6009).
文摘A queueing model of the Markov-modulated Poisson process (MMPP) with thresholds was investigated. The customer arrival with various arrival rates in the model was viewed as the MMPP. In contrast to the Poisson, s arrival process, the MMPP can better describe the situation that the arrival rate changes with changing conditions;therefore, the model fits better with reality. The threshold conversion was added to the model based on the general MMPP/M/C model. When the number of customers in the system exceeds a threshold, all servers work to serve;when the number of customers in the system is less than another threshold, some servers are shut down. This is the congestion-based staffing policy with two thresholds. Specifically, the problems in the slab stocking stage of slab production at the Iron and Steel Complex in China were analysed. In the slab production process, because the rate of the upstream steelmaking is not constant, the rate of slab reaching the slab yard is uncertain. The crane service is used to store slabs in a warehouse. Because the slab arrival rate varies, different numbers of cranes in service need to be optimized for cost control. Thus, MMPP was used to describe slab arrival with varied arrival rates. Therefore, an MMPP/M/C queue with thresholds was used to analyse and solve the practical problems, and the optimal number of service cranes was obtained to minimize the cost of slab stocking.
文摘The paper presents a new leaky--bucket (LB) model with Markov chain pattern of token generation and traffic arrival. The performance of the new LB model is analyzed in ATM networks. Finally, some results and useful conclusions are given.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11271287）.
文摘A pricing model for a corporate bond with rating migration risk is established in this article. With the technology of utility-indifference valuation under the Markov-modulated framework, we analyze the price of a multi-rating bond and obtain closed formulae in a three-rating case. Based on the pricing formulae, the impacts of the parameters on the indifference price are analyzed and some reasonable financial explanations are provided as well.
