The Joint Law of the Extrema, Final Value and Signature of a Stopped Random Walk

DOI10.1007/978-3-319-18585-9_15zbMath1336.60088arXiv1403.0220OpenAlexW2262001009MaRDI QIDQ2798586

Moritz Duembgen, L. C. G. Rogers

Publication date: 13 April 2016

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.0220

zbMATH Keywords

stopping timerandom walkextremacontinuous martingalesfinal valuerobust hedging strategies

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Sums of independent random variables; random walks (60G50) Stopping times; optimal stopping problems; gambling theory (60G40) Martingales with continuous parameter (60G44) Financial applications of other theories (91G80)

Related Items (3)

PDE for the joint law of the pair of a continuous diffusion and its running maximum ⋮ Pathwise superhedging for time-dependent barrier options on càdlàg paths -- finite or infinite tradeable European, one-touch, lookback or forward starting options ⋮ On joint distributions of the maximum, minimum and terminal value of a continuous uniformly integrable martingale

Cites Work

• Robust pricing and hedging of double no-touch options
• The joint law of the maximum and terminal value of a martingale
• A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options
• Robust Hedging of Barrier Options
• ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS
• A solution to Skorokhod's embedding for linear Brownian motion and its local time
• The maximum maximum of a martingale constrained by an intermediate law
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