Related papers: Efficient Discretization of Stochastic Integrals
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…
Optimal control of heterogeneous mean-field stochastic differential equations with common noise has not been addressed in the literature. In this work, we initiate the study of such models. We formulate the problem within a linear-quadratic…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression,…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…
We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
We propose an alternative approach towards cost mitigation in volatility-managed portfolios based on smoothing the predictive density of an otherwise standard stochastic volatility model. Specifically, we develop a novel variational Bayes…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…