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Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Model
Shortfall Risk Approximations American Options multidimensional Black--Scholes Model
2010/10/19
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar Ame...
Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear Black-Scholes equations
Transformation methods evaluating approximations optimal exercise boundary linear nonlinear Black-Scholes equations
2010/12/17
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla opti...
Optimal investment and consumption in a Black--Scholes market with Lévy-driven stochastic coefficients
Optimal investment consumption Black--Scholes market Lévy-driven stochastic coefficients
2010/12/20
In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black--Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornst...
Risk Premium Impact in the Perturbative Black Scholes Model
Risk Premium Impact Perturbative Black Scholes Model
2010/12/20
We study the risk premium impact in the Perturbative Black Scholes model. The Perturbative Black Scholes model, developed by Scotti, is a subjective volatility model based on the classical Black Schol...
From Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizon
Black-Scholes Dupire formulae last passage times local martingales Part A infinite time horizon
2010/12/20
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first aut...