Related papers: A Dual Method For Backward Stochastic Differential…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…
This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are `correct'. We draw the distinction between `external' and…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing…
In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the…
The present paper addresses the issue of the stochastic control of the optimal dynamic reinsurance policy and dynamic dividend strategy, which are state-dependent, for an insurance company that operates under multiple insurance lines of…
This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
This paper bridges reinforcement learning (RL) and risk-sensitive stochastic control by introducing a tractable exploration mechanism for policy search in risk-sensitive portfolio management, with known and unknown model parameters, that…
We investigate the test risk of continuous-time stochastic gradient flow dynamics in learning theory. Using a path integral formulation we provide, in the regime of a small learning rate, a general formula for computing the difference…
We introduce forward-backward stochastic differential equations, highlighting the connection between solutions of these and solutions of partial differential equations, related by the Feynman-Kac theorem. We review the technique of…
Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires…
We introduce a simple but powerful technique to study processes driven by two or more reinforcement mechanisms in competition. We apply our method to two types of models: to non conservative zero range processes on finite graphs, and to…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…