A Random Walk in Illiquidity Modeling

Rough volatility, subdiffusions, fractional Hawkes, optimal liquidation and deep learning

Liquidity is a fundamental property of a well-functioning financial market and lack of liquidity is generally at the heart of many financial crises and disasters, such as the global financial crisis of 2007–2008 and the LTCM crisis of 1998. Liquidity refers more precisely to the efficiency or ease with which an asset or security can be sold in financial markets without affecting its market price and is always tied to the temporal granularity at which it is analyzed. Indeed, when modeling the price of an asset and its liquidity, we typically distinguish between at least three different time scales: highfrequency (fraction of seconds), intraday time scale (between seconds and hours) and low-frequency (from days to years for very large time scales). These three temporalities and their connections are the subject of the three parts constituting this thesis. The first part of the thesis hence deals with rough volatility as it arises from the modelling of market liquidity at high frequency and studies the connection of such models with longterm insurance/asset pricing in Chapter 1 and with portfolio insurance strategies in Chapter 2. The second part of the thesis then investigates the use of fractional processes for modelling the illiquidity process associated with low-frequency observations of asset prices; first with subdiffusions in Chapter 3 and then with a new fractional Hawkes process in Chapter 4. Finally, the third part of the thesis focuses on stochastic optimal control in finance, and more precisely on optimal liquidation problems as they consider an intermediate time scale. A new jump-dependent indirect price impact model is then proposed in Chapter 5, and a deep learning algorithm is developed in Chapter 6 for solving complex high-dimensional stochastic optimal control (and liquidation) problems without explicit solution.


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Spécifications


Éditeur
Presses universitaires de Louvain
Auteur
Jean-Loup Dupret,
Collection
Thèses de la Faculté des sciences
Langue
anglais
Catégorie (éditeur)
Sciences exactes > Mathématiques > Probabilités et statistiques
Catégorie (éditeur)
Sciences exactes
BISAC Subject Heading
MAT000000 MATHEMATICS > MAT029000 MATHEMATICS / Probability & Statistics
BIC subject category (UK)
P Mathematics & science > PB Mathematics > PBT Probability & statistics
Code publique Onix
06 Professionnel et académique
CLIL (Version 2013-2019 )
3052 Mathématiques > 3056 Probabilités et statistiques
Date de première publication du titre
29 janvier 2025
Type d'ouvrage
Thèse

Livre broché


Date de publication
29 janvier 2025
ISBN-13
978-2-39061-477-7
Ampleur
Nombre de pages de contenu principal : 292
Dépôt Légal
D/2024/9964/22 Louvain-la-Neuve, Belgique
Code interne
107096
Format
16 x 24 cm
Poids
469 grammes
Type de packaging
Aucun emballage extérieur
Prix
33,00 €
ONIX XML
Version 2.1, Version 3

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Sommaire


Introduction 1
I Rough volatility modeling 9
1 Impact of rough stochastic volatility models on long-term life insurance pricing 11
2 Portfolio insurance under rough volatility and Volterra processes 53
3 A subdiffusive stochastic volatility jump model 91
4 A fractional Hawkes process for illiquidity modeling 135
5 Optimal liquidation under indirect price impact with propagator 179
6 Deep learning for high-dimensional stochastic optimal control without explicit solution 219
Conclusion and extensions 257
References 261