scholarly journals Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion

2019 ◽  
Vol 24 (2) ◽  
pp. 615-635
Author(s):  
Litan Yan ◽  
◽  
Xiuwei Yin ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Error Estimates ◽  
Stochastic Partial Differential Equation ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Partial Differential

scholarly journals Asian Option Pricing with Transaction Costs and Dividends under the Fractional Brownian Motion Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yan Zhang ◽  
Di Pan ◽  
Sheng-Wu Zhou ◽  
Miao Han
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Asian Option ◽  
Partial Differential ◽  
No Arbitrage ◽  
Geometric Average ◽  
Brownian Motion Model

The pricing problem of geometric average Asian option under fractional Brownian motion is studied in this paper. The partial differential equation satisfied by the option’s value is presented on the basis of no-arbitrage principle and fractional formula. Then by solving the partial differential equation, the pricing formula and call-put parity of the geometric average Asian option with dividend payment and transaction costs are obtained. At last, the influences of Hurst index and maturity on option value are discussed by numerical examples.

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