Stochastic Portfolio Theory and Otto Calculus
Stochastic Portfolio Theory and Otto Calculus
Disciplines
Mathematics (100%)
Keywords
-
Transaction Costs,
Otto calculus,
Optimal Transport Theory,
Stochastic Analysis,
Stochastic Portfolio Theory
A classical problem in Mathematical Finance is the topic of portfolio optimization. An investor tries to distribute her investment among many possible stocks in a smart way (think, e.g., of the 500 stocks listed in the S&P 500 index). The challenge is to find an investment strategy, where trading in these stocks takes place in continuous time, which satisfies some some optimality criterion such as expected long term growth. The latter criterion can be cast into precise and well-defined mathematical terms. Stochastic portfolio theory, as pioneered by R. Fernholz and Y. Karatzas some 20 years ago, relies on ideas originating in physics, namely interacting particle systems, to model the price dynamics of a large number of stocks. The current project develops a stochastic trajectorial approach to these models and applies this approach to the optimization problems arising in stochastic portfolio theory.
- Universität Wien - 100%
Research Output
- 9 Publications
- 6 Scientific Awards
-
2023
Title SDEs with no strong solution arising from a problem of stochastic control DOI 10.1214/23-ejp995 Type Journal Article Author Cox A Journal Electronic Journal of Probability -
2023
Title Existence of Bass martingales and the martingale Benamou$-$Brenier problem in $\mathbb{R}^{d}$ DOI 10.48550/arxiv.2306.11019 Type Preprint Author Backhoff-Veraguas J Link Publication -
2023
Title Faking Brownian motion with continuous Markov martingales DOI 10.1007/s00780-023-00526-w Type Journal Article Author Beiglböck M Journal Finance and Stochastics -
2023
Title The Bass functional of martingale transport DOI 10.48550/arxiv.2309.11181 Type Preprint Author Backhoff-Veraguas J Link Publication -
2023
Title Diffusion processes as Wasserstein gradient flows via stochastic control of the volatility matrix DOI 10.48550/arxiv.2310.18678 Type Preprint Author Tschiderer B Link Publication -
2022
Title Adapted Wasserstein distance between the laws of SDEs DOI 10.48550/arxiv.2209.03243 Type Preprint Author Backhoff-Veraguas J -
2024
Title Faking Brownian motion with continuous Markov martingales DOI 10.3929/ethz-b-000649552 Type Other Author Beiglböck Link Publication -
2022
Title SDEs with no strong solution arising from a problem of stochastic control DOI 10.48550/arxiv.2205.02519 Type Preprint Author Cox A -
2022
Title A regularized Kellerer theorem in arbitrary dimension DOI 10.48550/arxiv.2210.13847 Type Preprint Author Pammer G
-
2025
Title Conference in honor of Prof. Elyes Jouini, Paris 4-5 June 2025 Type Personally asked as a key note speaker to a conference Level of Recognition Continental/International -
2024
Title Colloquium talk Type Personally asked as a key note speaker to a conference Level of Recognition Continental/International -
2023
Title Invited Minisymposium Talk - SIAM Conference on Financial Mathematics and Engineering Type Personally asked as a key note speaker to a conference Level of Recognition Continental/International -
2023
Title Keynote speaker at RiO2023, Rio de Janeiro, Brasil Type Personally asked as a key note speaker to a conference Level of Recognition Continental/International -
2022
Title Invited speaker at Workshop "Stochastic Control and Quantitative Finance", Jerusalem Type Personally asked as a key note speaker to a conference Level of Recognition Continental/International -
2022
Title Invited talk at Conference in Memory of Tomas Björk "Some novelties on the laws of large numbers" Type Personally asked as a key note speaker to a conference Level of Recognition Continental/International