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Some remarks on first passage of Lévy processes, the American put and pasting principles
 Annals of Appl. Probability
"... The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Lévy process and the solution of Gerber and Shiu [Astin ..."
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The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Lévy process and the solution of Gerber and Shiu [Astin
Analyticity of the Wiener–Hopf factors and valuation of exotic options in Lévy models. Working paper
, 2009
"... Abstract. This paper considers the valuation of exotic pathdependent options in Lévy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener–Hopf factorization, we derive expressions for the analytically extended characteristic function of the supr ..."
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Abstract. This paper considers the valuation of exotic pathdependent options in Lévy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener–Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a Lévy process. Combined with general results on Fourier methods for option pricing, we provide formulas for the valuation of onetouch options, lookback options and equity default swaps in Lévy models. 1.
MATURITY RANDOMIZATION FOR STOCHASTIC CONTROL PROBLEMS
, 2006
"... We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the socalled Canadization procedure suggested by Carr [Revie ..."
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We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the socalled Canadization procedure suggested by Carr [Review of Financial Studies II (1998) 597–626] for the fast computation of American put option prices. In addition to the original application of this technique to optimal stopping problems, we provide an application to another problem in finance, namely the superreplication problem under stochastic volatility, and we show that the approximating value functions can be computed explicitly. 1. Introduction. It
Chapter 2 JumpDiffusion Models for Asset Pricing in Financial Engineering
 In: Handbooks in Operations Research and Management
, 2007
"... In this survey we shall focus on the following issues related to jumpdiffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a riskneutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace ..."
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In this survey we shall focus on the following issues related to jumpdiffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a riskneutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, pathdependent options, such as barrier and lookback options. (4) Difficulties associated with the partial integrodifferential equations related to barriercrossing problems. (5) Analytical approximations for finitehorizon American options with jump risk. (6) Multivariate jumpdiffusion models. 1
OPTIMAL STOPPING PROBLEMS FOR SOME MARKOV PROCESSES
"... In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of onesided regular Feller processes. This generalizes the result of Beibel and Lerche ..."
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In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of onesided regular Feller processes. This generalizes the result of Beibel and Lerche [4, 5] and Paulsen [13]. Our approach relies on a combination of techniques borrowed from potential theory and stochastic calculus. We illustrate our results by detailing some new examples ranging from linear diffusions to Markov processes of the spectrally negative type.