The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an...The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.展开更多
In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the...In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14<sup>th</sup> March 2020 to 1<sup>st</sup> February 2021. The first wave was experienced from 14<sup>th</sup> March 2020 to 15<sup>th</sup> September 2020, the second wave from around 15<sup>th</sup> September 2020 to 1<sup>st</sup> February 2021 and the third wave was experienced from 1<sup>st</sup> February 2021 to 3<sup>rd</sup> June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.展开更多
文摘The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.
文摘In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14<sup>th</sup> March 2020 to 1<sup>st</sup> February 2021. The first wave was experienced from 14<sup>th</sup> March 2020 to 15<sup>th</sup> September 2020, the second wave from around 15<sup>th</sup> September 2020 to 1<sup>st</sup> February 2021 and the third wave was experienced from 1<sup>st</sup> February 2021 to 3<sup>rd</sup> June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.
