As one of the major methods for the simulation of option pricing,Monte Carlo method assumes random fluctuations in the distribution of asset prices.Under certain uncertainties process,different evolution paths could b...As one of the major methods for the simulation of option pricing,Monte Carlo method assumes random fluctuations in the distribution of asset prices.Under certain uncertainties process,different evolution paths could be simulated so as to finally yield the expectation value of the asset price,which requires a lot of simulations to ensure the accuracy based on huge and expensive calculations.In order to solve the above computational problem,quantum Monte Carlo(QMC)has been established and applied in the relevant systems such as European call options.In this work,both MC and QM methods are adopted to simulate European call options.Based on the preparation of quantum states in QMC algorithm and the construction of quantum circuits by simulating a quantum hardware environment on a traditional computer,the amplitude estimation(AE)algorithm is found to play a secondary role in accelerating the pricing of European options.More importantly,the payoff function and the time required for the simulation in QMC method show some improvements than those in MC method.展开更多
This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounde...This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.展开更多
基金This work was financially supported by the National Natural Science Foundation of China Granted No.11764028。
文摘As one of the major methods for the simulation of option pricing,Monte Carlo method assumes random fluctuations in the distribution of asset prices.Under certain uncertainties process,different evolution paths could be simulated so as to finally yield the expectation value of the asset price,which requires a lot of simulations to ensure the accuracy based on huge and expensive calculations.In order to solve the above computational problem,quantum Monte Carlo(QMC)has been established and applied in the relevant systems such as European call options.In this work,both MC and QM methods are adopted to simulate European call options.Based on the preparation of quantum states in QMC algorithm and the construction of quantum circuits by simulating a quantum hardware environment on a traditional computer,the amplitude estimation(AE)algorithm is found to play a secondary role in accelerating the pricing of European options.More importantly,the payoff function and the time required for the simulation in QMC method show some improvements than those in MC method.
基金supported by National Science Foundation for Distinguished Young Scholars of China (Grant No. 10925107)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2011)
文摘This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.
