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Asymptotic approaches in financial risk management

Abstract : This thesis focuses on three problems from the area of financial risk management, using various asymptotic approaches. The first part presents an importance sampling algorithm for Monte Carlo pricing of exotic options in exponential Lévy models. The optimal importance sampling measure is computed using techniques from the theory of large deviations. The second part uses the Laplace method to study the tail behavior of the sum of n dependent positive random variables, following a log-normal mixture distribution, with applications to portfolio risk management. Finally, the last part employs the notion of multivariate regular variation to analyze the tail behavior of a random vector with heavy-tailed components, whose dependence structure is modeled by a Gaussian copula. As application, we consider the tail behavior of a portfolio of options in the Black-Scholes model
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Submitted on : Wednesday, November 13, 2019 - 1:28:22 PM
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Adrien Genin. Asymptotic approaches in financial risk management. General Mathematics [math.GM]. Université Sorbonne Paris Cité, 2018. English. ⟨NNT : 2018USPCC120⟩. ⟨tel-02361422⟩



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