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Scaling properties of first-passage time probabilities in financial markets
Scaling properties first-passage time probabilities financial markets
2011/7/19
Financial markets provide an ideal frame for the study of first-passage time events of non-
Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures...
Default Risk Modeling Beyond the First-Passage Approximation: Extended Black-Cox Model
Default Risk Modeling the First-Passage Approximation Extended Black-Cox Model
2010/10/18
We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm's ability to avoid default even if company's liabilities momentar...
First-passage and risk evaluation under stochastic volatility
First-passage risk evaluation
2010/10/29
We solve the first-passage problem for the Heston random diffusion model. We obtain exact
analytical expressions for the survival and hitting probabilities to a given level of return. We study severa...
The first passage event for sums of dependent Lévy processes with applications to insurance risk
First passage event fluctuation theory ladder process multivariate L´ evy process
2010/11/3
For the sum process X = X1 + X2 of a bivariate L´evy process (X1,X2) with possibly dependent components, we derive a quintuple law describing the first upwards passage event of X over a fixed ba...
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...
On perpetual American put valuation and first-passage in a regime-switching model with jumps
perpetual American valuation first-passage regime-switching model jumps
2010/12/17
In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching L\'{e}vy model. For the case of the (dense) class of phase-type jumps and finitely ...
In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatil-ity ideally associated with a scenario base...