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Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization ofrandomly varying volatility. The rec...
We introduce a class of local stochastic volatility models.Within our framework, we obtain an expression for both (i) the price of any European option and (ii) the induced implied volatility smile. To...
We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We pro...
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pri...
Agents' heterogeneity has been recognized as a driver mechanism for the persistence of nancial volatility. We focus on the multiplicity of investment strategies' horizons;we embed this concept in a c...
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting...
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson a...
Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method...
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that th...
We prove stochastic representation formulae for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our artic...
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a gene...
The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartin-gale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The propert...
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simul...
We extend Kirman's model by introducing variable event time scale. The proposed exi- ble time scale is equivalent to the variable trading activity observed in nancial markets. Stochastic version ...

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