In this paper, a pricing problem of European call options is considered, wbete the underlying stock generates dividends d, at some fixed future dates T, before the expiration date T .without the inappropriate assumpti...In this paper, a pricing problem of European call options is considered, wbete the underlying stock generates dividends d, at some fixed future dates T, before the expiration date T .without the inappropriate assumption made in that the dlvkdeMs being payed continously.The arbitrage free pricing of the option is determined via a series of partial differential equations.which is derived at the view point of backward s'tochasric differential ertuation (BBDE). It isshowed how the dividends affect the fair price of the call options. Some simulating results are alsogiven to illust rate the respective in fluence of parameters a.T.r,K.di and F1 on the option pricing.展开更多
In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered, for an investor who has available a bank account and a stock whose price is a log normal di...In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered, for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r for any deposit, and takes at a larger rate r′ for any loan. As in the paper of Xu Wensheng and Chen Shuping in JAMS(B), where an analogous problem in finite horizon is studied, optimal strategies are obtained via Hamilton Jacobi Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, i.e. U(t,c)=e -βt c 1-R 1-R , this paper gets the optimal consumption and optimal investment in the form ofc * t=β-Rw t\ and \ π * t=b-γRσ 2w twith γ:= max{ r, min{ r′,b-Rσ 2 }}, =(1-R)γ+(b-γ) 22Rσ 2]. This result coincides with the classical one under condition r′≡r.展开更多
文摘In this paper, a pricing problem of European call options is considered, wbete the underlying stock generates dividends d, at some fixed future dates T, before the expiration date T .without the inappropriate assumption made in that the dlvkdeMs being payed continously.The arbitrage free pricing of the option is determined via a series of partial differential equations.which is derived at the view point of backward s'tochasric differential ertuation (BBDE). It isshowed how the dividends affect the fair price of the call options. Some simulating results are alsogiven to illust rate the respective in fluence of parameters a.T.r,K.di and F1 on the option pricing.
文摘In this paper, optimal investment and consumption decisions for an optimal choice problem in infinite horizon are considered, for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r for any deposit, and takes at a larger rate r′ for any loan. As in the paper of Xu Wensheng and Chen Shuping in JAMS(B), where an analogous problem in finite horizon is studied, optimal strategies are obtained via Hamilton Jacobi Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, i.e. U(t,c)=e -βt c 1-R 1-R , this paper gets the optimal consumption and optimal investment in the form ofc * t=β-Rw t\ and \ π * t=b-γRσ 2w twith γ:= max{ r, min{ r′,b-Rσ 2 }}, =(1-R)γ+(b-γ) 22Rσ 2]. This result coincides with the classical one under condition r′≡r.
