On the Skew and Curvature of the Implied and Local Volatilities [PDF]
Applied Mathematical Finance, 2022 In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent rule (where H denotes the Hurst parameter of the volatility process ...
E. Alòs +2 more
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Understanding Reinforcement Learning Algorithms: The Progress from Basic Q-learning to Proximal Policy Optimization [PDF]
arXiv.org, 2023 This paper presents a review of the field of reinforcement learning (RL), with a focus on providing a comprehensive overview of the key concepts, techniques, and algorithms for beginners.
M. Chadi, H. Mousannif
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Sig-SDEs model for quantitative finance [PDF]
International Conference on AI in Finance, 2020 Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance. In this work, we propose a novel framework for data-driven model selection by integrating a classical quantitative setup with a
Imanol Perez Arribas +2 more
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Adapted Wasserstein distances and stability in mathematical finance [PDF]
Finance and Stochastics, 2019 Assume that an agent models a financial asset through a measure ℚ with the goal to price/hedge some derivative or optimise some expected utility.
J. Backhoff‐Veraguas +3 more
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Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks [PDF]
Physical Review Research, 2020 In this paper we tackle the problem of dynamic portfolio optimization, i.e., determining the optimal trading trajectory for an investment portfolio of assets over a period of time, taking into account transaction costs and other possible constraints ...
Samuel Mugel +6 more
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A model-free approach to continuous-time finance [PDF]
Mathematical Finance (2023), 2022 We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral (every self-financing strategy is a gradient) and that generic domain of functional ...
arxiv +1 more source
On absolute continuity and singularity of multidimensional diffusions [PDF]
, 2020 Consider two laws \(P\) and \(Q\) of multidimensional possibly explosive diffusions with common diffusion coefficient \(\mathfrak{a}\) and drift coefficients \(\mathfrak{b}\) and \(\mathfrak{b} + \mathfrak{a} \mathfrak{c}\), respectively, and the law \(P^
D. Criens
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The W, Z scale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems [PDF]
E S A I M: Probability & Statistics, 2017 In the last years there appeared a great variety of identities for first passage problems of spectrally negative Lévy processes, which can all be expressed in terms of two “q-harmonic functions” (or scale functions) W and Z.
F. Avram, D. Grahovac, Ceren Vardar-Acar
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Complete and competitive financial markets in a complex world [PDF]
Finance and Stochastics 2021, 2020 We investigate the possibility of completing financial markets in a model with no exogenous probability measure and market imperfections. A necessary and sufficient condition is obtained for such extension to be possible.
arxiv +1 more source
The Role of Hellinger Processes in Mathematical Finance
Entropy, 2001 This paper illustrates the natural role that Hellinger processes can play in solving problems from ¯nance. We propose an extension of the concept of Hellinger process applicable to entropy distance and f-divergence distances, where f is a convex ...
Tahir Choulli, T. Hurd
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