Optimal stopping and perpetual options for Lévy processes

By Ernesto Mordecki. 2002

262 citations recorded by the source corpus.

Subfields: Demography, Finance, Management Science and Operations Research

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Citations in the corpus

Option Pricing Under a Double Exponential Jump Diffusion Model (2004, background): “6 See, for example, Siegmund (1985), Boyarchenko and Levendorskiı̆ (2002b), and Kyprianou and Pistorius (2003) for some representations (though not explicit calculations) related to the overshoot problems for general Lévy processes.”
WIENER-HOPF FACTORIZATION FOR LEVY PROCESSES HAVING POSITIVE JUMPS WITH RATIONAL TRANSFORMS (2008, background): “stopping problem related to the pricing of a perpetual call and put option, respectively, in a market model generated by a Lévy process (see [7] and [18]).”
Symmetry and duality in Lévy markets (2006, methodology): “S p 1⁄4 S0 ~ Ee ~ I , as follows from Theorem 2 in Mordecki (2002). We express this quantity in the risk-neutral market:”
Fractional Diffusion Models of Option Prices in Markets With Jumps (2007, background): “The case T 1⁄4 1 is known as a perpetual option and closed-form solutions may be obtained for a large class of members of the Lévy processes family [32,33].”
Some remarks on first passage of Levy processes, the American put and pasting principles (2005, unknown): “ar X iv :m at h/ 05 08 48 7v 1 [ m at h. PR ] 2 5 A ug 2 00 5 The Annals of Applied Probability 2005, Vol. 15, No. 3, 2062–2080 DOI: 10.1214/105051605000000377 c© Institute of Mathematical Statistics, 2005”
Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes (2007, background): “Such a model was considered in [12], [13], [17]–[19], [20], and [21], where some one-dimensional optimal stopping problems were solved.”
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, background): “Howevery in recent years there is also a growing interest in applications of Wiener-Hopf factorization, for example in Mathematical Finance, where the above mentioned functionals are being used to describe the payoff of a contract and the corresponding probability distribution is used to compute its”
Barrier options and touch- and-out options under regular Lévy processes of exponential type (2002, background): “Later, Mordecki (2000) obtained pricing formulas for perpetual American puts and calls by using the probabilistic technique, but without explicit analytic formulas for processes observed in financial markets; his method allows one neither to notice the failure of the smooth fit principle nor to…”
Fisher's Information for Discretely Sampled Lévy Processes (2004, background): “…in mathematical finance, for instance in option pricing [see e.g., Eberlein and Jacod (1997), Chan (1999), Boyarchenko and Levendorskii (2002), Mordecki (2002) and Carr and Wu (2004)], testing for the presence of jumps in asset prices [see Aı̈t–Sahalia (2002) and Carr and Wu (2003)], interest…”
Optimal stopping of Hunt and Lévy processes (2006, result): “These results are generalized for Lévy process by Mordecki in Refs [15] and [16], where it is also observed that similar results hold for solutions of optimal stopping problems in terms of the infimum of the process for the payoff gðxÞ 1⁄4 ð12 exÞþ.”
Sample Efficient Policy Search for Optimal Stopping Domains (2017, background): “…the secretary problem [Fer-guson, 1989], house selling [Glower et al. , 1998; Lippman and McCall, 1976], American options trading [Jacka, 1991; Mordecki, 2002], product pricing [Feng and Gallego, 1995] and asset replacement [Jiang and Powell, 2015], as well as problems in artiﬁcial…”
A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, background): “Mordecki (2002) and Lipton (2002) calculated the Laplace transforms of first-passage time distributions for a Lévy process with hyper-exponential jumps.”
The McKean stochastic game driven by a spectrally negative Lévy process (2008, background): “When X has a Gaussian component, recall from (22) that V (log K+) − V (log K−) = 2 σ2 αe K−x ) > 0”
Russian and American put options under exponential phase-type Lévy models (2004, unknown): “Mordecki [40] has shown that, for a general Lévy process X, U∗(x) = IEx[e−δT ∗ (K − eXT∗ )], where the optimal stopping time T ∗ is given by the first passage time of the process X below the level k∗, T ∗ = T (k∗) = inf{t ≥ 0 : Xt ≤ k∗}, (7) where exp(k∗) = K IE[eδ ].”
Using Brownian Bridge for Fast Simulation of Jump-Diffusion Processes and Barrier Options (2002, methodology): “Based on this, an analytical formula for barrier options under the standard lognormal process has been derived (Hull [1997], Wilmott [1998]).”