We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approa...We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.展开更多
This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonli...This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.展开更多
The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modu...The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.展开更多
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov...A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.展开更多
This paper considers a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable.A two-step approach to estimate the drift function of a jump-diffusion mo...This paper considers a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable.A two-step approach to estimate the drift function of a jump-diffusion model in noisy settings is proposed.The proposed estimator is shown to be consistent and asymptotically normal in the presence of finite activity jumps.Simulated experiments and a real data application are undertaken to assess the finite sample performance of the newly proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(No.11571365,11171349)
文摘We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.
基金supported by the National Natural Science Foundation of China(Nos.10921101,11471190)the Shandong Provincial Natural Science Foundation of China(No.ZR2014AM002)the Programme of Introducing Talents of Discipline to Universities of China(No.B12023)
文摘This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.
基金Supported by the National Natural Science Foundation of China(No.11301454,No.71771147 and No.71201100)the Jiangsu Qing Lan Project for Excellent Young Teachers in University(2014)+1 种基金Six Talent Peaks Project in Jiangsu Province(2016-JY-081)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020)
文摘The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.
文摘A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.
基金the National Natural Science Foundation of China under Grant No.11961038Cultivating Project of National Natural Science Foundation(QianKeHe talent-development platform[2017]No.5723,QianKeHe talent-development platform[2017]No.5723-02)+7 种基金supported by the National Natural Science Foundation of China under Grant Nos.12071220,11701286supported by the National Natural Science Foundation of China under Grant Nos.11831008,11971235Young Talents Project of Science and Technology Research Program of Education Department in Guizhou Province(Qianjiao KYword[2018]364)Science and Technology Foundation of Guizhou Province(QianKeHejichu[2019]1286)Social Science Foundation of Jiangsu Province under Grant No.20EYC008the National Statistical Research Project of China under Grant No.2020LZ35the National Statistical Research Project of China under Grant No.2020LZ19Open Project of Jiangsu Key Laboratory of Financial Engineering under Grant No.NSK2021-12。
文摘This paper considers a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable.A two-step approach to estimate the drift function of a jump-diffusion model in noisy settings is proposed.The proposed estimator is shown to be consistent and asymptotically normal in the presence of finite activity jumps.Simulated experiments and a real data application are undertaken to assess the finite sample performance of the newly proposed method.
