It is well known that backward stochastic di erential equations (BSDEs) stem from the study on the Pontryagin type maximum principle for optimal stochastic controls. A solution of a BSDE hits a given terminal value (which is a random variable) by virtue of an additional martingale term and an inde nite initial state. This paper attempts to view the relation between BSDEs and stochastic controls...

We study an incompletely parabolic system in three space dimensions with stochastic boundary and initial data. We show how the variance of the solution can be manipulated by the boundary conditions, while keeping the mean value of the solution unaffected. Estimates of the variance of the solution is presented both analytically and numerically. We exemplify the technique by applying it to an inc...

There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves planning in an infinitely large tree. However, it is possible to obtain lower and stochastic upper bounds on the value of each tree node. This enables us to use sto...

We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is pre-specified. The analysis of such control problems is motivated by models ...

The oil industry is increasingly interested in improving the planning of their operations due to the dynamic nature of this business. Decisions made at the oil chain differ in the activity range (spatial integration) and planning horizon (temporal integration). This paper purpose is to address the spatial integration under uncertainty in the oil chain at the tactical planning level and proposes...

We present a finite element method for the numerical solution of elliptic boundary value problems on stochastic domains. The method computes, to leading order in the amplitude of the stochastic boundary perturbation relative to an unperturbed, nominal domain, the mean and the variance of the random solution. The variance is computed as the trace of the solution’s two-point correlation which sat...

We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixedinteger programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear descriptio...

We study a stochastic version of Fudenberg–Tirole’s preemption game. Two firms contemplate entering a new market with stochastic demand. Firms differ in sunk costs of entry. If the demand process has no upward jumps, the low cost firm enters first, and the high cost firm follows. If leader’s optimization problem has an interior solution, the leader enters at the optimal threshold of a monopolis...