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Lagrange regularization approach to compare nested data sets and determine objectively financial bubbles' inceptions
Demos, Guilherme; Sornette, Didier - 2017
Inspired by the question of identifying the start time τ of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange...
Persistent link: https://www.econbiz.de/10011877499
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A result on integral functionals with infinitely many constraints
Choulli, Tahir; Schweizer, Martin - 2015 - This version: 14.09.2015
A classic paper of Borwein/Lewis (1991) studies optimisation problems over L^p_+ with finitely many linear equality constraints, given by scalar products with functions from L^q. One key result shows that if some x in L^p_+ satisfies the constraints and if the constraint functions are...
Persistent link: https://www.econbiz.de/10011412336
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Properly discounted asset prices are semimartingales
Bálint, Dániel Ágoston; Schweizer, Martin - 2019 - This version: October 3, 2019
We study general undiscounted asset price processes, which are only assumed to be non- negative, adapted and RCLL (but not a priori semimartingales). Traders are allowed to use simple (piecewise constant) strategies. We prove that under a discounting-invariant condition of absence of arbitrage,...
Persistent link: https://www.econbiz.de/10012134260
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Martingale optimal transport in the Skorokhod space
Dolinsky, Yan; Soner, Halil Mete - 2014
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag …
Persistent link: https://www.econbiz.de/10011293818
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Locally phi-integrable sigma-martingale densities for general semimartingales
Choulli, Tahir; Schweizer, Martin - 2015 - This version: 22.5.2015
A P-sigma-martingale density for a given stochastic process S is a local P-martingale Z>0 starting at 1 such that the … product ZS is a P-sigma-martingale. Existence of a P-sigma-martingale density is equivalent to a classic absence … there exists a P-sigma-martingale density for S. Can we find another P-sigma-martingale density for S having some extra …
Persistent link: https://www.econbiz.de/10011296922
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Deep learning for asset bubbles detection
Bashchenko, Oksana; Marchal, Alexis - 2020
We develop a methodology for detecting asset bubbles using a neural network. We rely on the theory of local martingales in continuous-time and use a deep network to estimate the diffusion coefficient of the price process more accurately than the current estimator, obtaining an improved detection...
Persistent link: https://www.econbiz.de/10012181227
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Uniform integrability of a single jump local martingale with state-dependent characteristics
Schatz, Michael; Sornette, Didier - 2017
We investigate a deterministic criterion to determine whether a diffusive local martingale with a single jump and state …-dependent characteristics is a uniformly integrable martingale. We allow the diffusion coefficient, the jump hazard rate and the relative jump … size to depend on the state and prove that the process is a uniformly integrable martingale if and only if the relative …
Persistent link: https://www.econbiz.de/10011762245
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Dynamic mean-variance optimisation problems with deterministic information
Schweizer, Martin; Zivoi, Danijel; Ṥikić, Mario - 2017 - This version: September 29, 2017
-information filtration and assume that S is a time-dependent affine transformation of a square-integrable martingale. This class of processes …
Persistent link: https://www.econbiz.de/10011865489
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Making no-arbitrage discounting-invariant : a new FTAP beyond NFLVR and NUPBR
Bálint, Dániel Ágoston; Schweizer, Martin - 2018 - This version: March 16, 2018
characterisations of our concepts in terms of martingale properties. A key new feature is that as one expects, “properly anticipated …
Persistent link: https://www.econbiz.de/10011899592
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Conditional Davis pricing
Larsen, Kasper; Soner, Halil Mete; Zitkovic, Gordan - 2018
We study the set of marginal utility-based prices of a financial derivative in the case where the investor has a non-replicable random endowment. We provide an example showing that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - the interval of marginal...
Persistent link: https://www.econbiz.de/10011899936