Data-Driven Non-Parametric Robust Control under Dependence Uncertainty
Erhan Bayraktar and
Tao Chen
Chapter 5 in Peter Carr Gedenkschrift:Research Advances in Mathematical Finance, 2023, pp 141-178 from World Scientific Publishing Co. Pte. Ltd.
Abstract:
We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the non-parametric adaptive robust control framework. We aim to find the optimal control against the worst-case copulae in a sequence of shrinking uncertainty sets which are generated from continuously observing the data. Then, we use a stochastic gradient descent ascent algorithm to numerically handle the corresponding high-dimensional dynamic inf-sup optimization problem. We present the numerical results in the context of utility maximization and show that the controller benefits from knowing more information about the uncertain model.
Keywords: Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures (search for similar items in EconPapers)
JEL-codes: C02 C6 (search for similar items in EconPapers)
Date: 2023
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Working Paper: Data-Driven Nonparametric Robust Control under Dependence Uncertainty (2022) 
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