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Weighted Monte Carlo: Calibrating the Smile and Preserving Martingale Condition
Monte Carlo exotic options the Martingale condition might geometric cliquet option
2011/3/23
Weighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options ...
Minimal $f$-divergence martingale measures and optimal portfolios for exponential Levy models with a change-point
f-divergence exponential Levy models
2010/10/19
We consider the exponential Levy models and we study the conditions under which f-minimal equivalent martingale measure preserves Levy property. Then we give a general formula for optimal strategy in...
Minimal $f$-divergence martingale measures and optimal portfolios for exponential Levy models with a change-point
f-divergence exponential Levy models change-point optimal portfolio
2010/4/28
We consider the exponential Levy models and we study the conditions under which f-minimal equivalent martingale measure preserves Levy property. Then we give a general formula for optimal strategy in ...
Martingale representation for Poisson processes with applications to minimal variance hedging
Martingale representation Poisson processes applications minimal variance hedging
2010/10/18
We consider a Poisson process $\eta$ on a measurable space $(\BY,\mathcal{Y})$ equipped with a partial ordering, assumed to be strict almost everwhwere with respect to the intensity measure $\lambda$...
On the Martingale Property of Certain Local Martingales
Local martingales vs true martingales one-dimensional diffusions separating times
2010/11/1
The stochastic exponential Zt = exp{Mt − M0 − (1/2)hM,Mit} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the ...
Strict Local Martingale Deflators and Pricing American Call-Type Options
Strict local martingales deflators American call options
2010/11/2
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question prop...
ARCH and GARCH Models vs. Martingale Volatility of Finance Market Returns
ARCH GARCH Models Martingale Volatility Finance Market Returns
2010/12/17
ARCH and GARCH models assume either i.i.d. or (what economists lable as) white noise as is usual in regression analysis while assuming memory in a conditional mean square fluctuation with stationary ...