Portfolio Optimization in Fractional and Rough Heston Models

DOI10.1137/18M1217243zbMath1437.91403arXiv1809.10716MaRDI QIDQ5112724

Sascha Desmettre, Nicole Bäuerle

Publication date: 8 June 2020

Published in: SIAM Journal on Financial Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.10716

zbMATH Keywords

Hamilton-Jacobi-Bellman equationstochastic controlrough pathsHeston modelfractional stochastic processesFeynman-Kac respresentation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic models in economics (91B70) Optimal stochastic control (93E20) Portfolio theory (91G10)

Related Items

Utility Maximization in Multivariate Volterra Models ⋮ Integral representation of generalized grey Brownian motion ⋮ Stochastic analysis for vector-valued generalized grey Brownian motion ⋮ Optimal reinsurance-investment with loss aversion under rough Heston model ⋮ Large deviations for fractional volatility models with non-Gaussian volatility driver ⋮ Mean-variance portfolio selection under Volterra Heston model ⋮ Markowitz Portfolio Selection for Multivariate Affine and Quadratic Volterra Models ⋮ Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge ⋮ Time-Inconsistency with Rough Volatility

Uses Software

• Matlab

Cites Work

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• Affine fractional stochastic volatility models
• Weak limit theorems for stochastic integrals and stochastic differential equations
• On a comparison theorem for solutions of stochastic differential equations and its applications
• Perfect hedging in rough Heston models
• Numerical solution of fractional differential equations: a survey and a software tutorial
• Moment explosions in the rough Heston model
• Stochastic control with rough paths
• Affine representations of fractional processes with applications in mathematical finance
• Stochastic calculus with respect to fractional Brownian motion
• Long memory in continuous-time stochastic volatility models
• Martingales versus PDEs in finance: an equivalence result with examples
• The Heston Model and Its Extensions in Matlab and C#
• Asymptotics for Rough Stochastic Volatility Models
• UTILITY MAXIMIZATION IN AFFINE STOCHASTIC VOLATILITY MODELS
• Asymptotic Behavior of the Fractional Heston Model
• Volatility is rough
• Optimal Portfolio under Fast Mean-Reverting Fractional Stochastic Environment
• System Control and Rough Paths
• Pricing under rough volatility
• Volatility Options in Rough Volatility Models
• Multifactor Approximation of Rough Volatility Models
• Optimal portfolio under fractional stochastic environment
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• PORTFOLIO OPTIMIZATION UNDER PARTIAL INFORMATION WITH EXPERT OPINIONS
• Optimal Portfolios for Financial Markets with Wishart Volatility
• Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility
• The characteristic function of rough Heston models
• A course on rough paths. With an introduction to regularity structures
• Approximation of some processes
• A solution approach to valuation with unhedgeable risks
• The maximum rate of convergence for the approximation of the fractional Lévy area at a single point