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Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme
BSDE FBSDE Four Step Scheme Asymptotic Expansion Malliavin Derivative Non-linear PDE CVA
2011/7/4
In this work, we have presented a simple analytical approximation scheme for the
generic non-linear FBSDEs. By treating the interested system as the linear decoupled
FBSDE perturbed with non-linear ...
Ruin probabilities in tough times - Part 2 - Heavy-traffic approximation for fractionally differentiated random walks in the domain of attraction of a nonGaussian stable distribution
heavy traffic ruin probability fractional random walk FARIMA process Poisson process
2011/3/23
Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as some FARIMA processe...
A New Approximation to the Normal Distribution Quantile Function
Normal Distribution Quantile Function
2010/10/18
We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2...
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...
A remark on Gatheral's 'most-likely path approximation' of implied volatility
remark on Gatheral's 'most-likely path implied volatility
2010/11/2
We give a rigorous proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we fix the problem of a circular defi...
Variance-covariance based risk allocation in credit portfolios: analytical approximation
Variance-covariance risk allocation nalytical approximation
2010/11/1
High precision analytical approximation is proposed for variance-covariance based risk allocation in a portfolio of risky assets. A general case of a single-period multi-factor Merton-type model with ...
Strong Taylor approximation of stochastic differential equations and application to the Lévy LIBOR model
LIBOR models stochastic differential equations L´ evy pro-cesses perturbation Taylor approximation caps, swaptions
2010/11/1
In this article we develop a method for the strong approx-imation of stochastic differential equations (SDEs) driven by L´evy pro-cesses or general semimartingales. The main ingredients of our m...
Maximum-Likelihood Estimation of Discretely-Sampled Diffusions: A Closed-Form Approximation Approach
Maximum-Likelihood Estimation Discretely-Sampled Diffusions A Closed-Form Approximation Approach
2014/3/13
Maximum-Likelihood Estimation of Discretely-Sampled Diffusions: A Closed-Form Approximation Approach.