By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series meth...By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series method.The classical problem on finding conditions on the polynomial coefficients P_(j)(z)(j=0,1,2)and F(z)to guarantee that all nontrivial solutions of complex second order difference equation P_(2)(z)f(z+2)+P_(1)(z)f(z+1)+P_(0)(z)f(z)=F(z)has slowly growing solutions with order 1/2 is detected.展开更多
The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow spee...The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow speed of convergence.On the basis of the PDE approach,we develop a consistent numerical scheme called the modified binomial tree method.It possesses one order of accuracy and its efficiency is demonstrated by numerical experiments.The convergence proofs are also produced in terms of numerical analysis and the notion of viscosity solution.展开更多
文摘By using asymptotic method,we verify the existence on the slowly growing solutions to second order difference equations discussed by Ishizaki-Yanagihara’s Wiman-Valiron method and Ishizaki-Wen’s binomial series method.The classical problem on finding conditions on the polynomial coefficients P_(j)(z)(j=0,1,2)and F(z)to guarantee that all nontrivial solutions of complex second order difference equation P_(2)(z)f(z+2)+P_(1)(z)f(z+1)+P_(0)(z)f(z)=F(z)has slowly growing solutions with order 1/2 is detected.
基金Supported by National Science Foundation of China (No.19871062)
文摘The binomial tree method is the most popular numerical approach to pricing options. However,for currency lookback options,this method is not consistent with the corresponding continuous models,which leads to slow speed of convergence.On the basis of the PDE approach,we develop a consistent numerical scheme called the modified binomial tree method.It possesses one order of accuracy and its efficiency is demonstrated by numerical experiments.The convergence proofs are also produced in terms of numerical analysis and the notion of viscosity solution.
