In this paper we study zero-sum two-player stochastic differential games with the help of theory of Backward Stochastic Differential Equations (BSDEs). At the one hand we generalize the results of the pioneer work of Fleming and Souganidis [8] by considering cost functionals defined by controlled BSDEs and by allowing the admissible control processes to depend on events occurring before the beg...

Milevsky and Huang (2011) investigated the optimal retirement spending policy for a utility-maximizing retiree facing a stochastic lifetime but assuming deterministic investment returns. They solved the problem using techniques from the calculus of variations and derived analytic expressions for the optimal spending rate and wealth depletion time under the Gompertz law of mortality. Of course, ...

This paper proposes an approximate dynamic programming-based method for optimizing the distribution operations of a company manufacturing a certain product in numerous plants and distributing it to different regional markets for sale. The production at each plant and in each time period follows a nonstationary stochastic process. The product can be stored at the plants or shipped to a regional ...

Traditional approaches to solving stochastic optimal control problems involve dynamic programming, and solving certain optimality equations. When recast as stochastic programming problems, structural aspects such as convexity are regained, and solution procedures based on decomposition and duality may be exploited. This paper explores a class of stationary, infinite-horizon stochastic optimizat...

To a large extent, electricity markets worldwide still rely on deterministic procedures for clearing energy and reserve auctions. However, larger and larger shares of the production mix consist of renewable sources whose nature is stochastic and non-dispatchable, as their output is not known with certainty and cannot be controlled by the operators of the production units. Stochastic programming...

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances (the achievable region) of the system of interest, and (ii) optimising the overall system-wide performance objective over this space. This is radically di erent from conventional formulations based on dynamic programming. The approach is explained with...

This research investigates the dynamics of capacity planning and dispatch in the US electric power sector under a range of technological, economic, and policy-related uncertainties. Using a twostage stochastic programming approach, model results suggest that the two most critical risks in the near-term planning process are natural gas prices and the stringency of climate policy. Stochastic stra...

In this study, we formulate a stochastic dynamic framework for pest control over the growing season taking into account forecasts of weather conditions and pest infestation expectations. Using stochastic envelope theorem and stochastic comparative dynamics, we analytically show how the stochastic correlation between the prediction errors should affect optimal pesticide usage path. As a case stu...

Electricity markets face a substantial amount of uncertainty. Traditionally this uncertainty has been due to varying demand. With the integration of larger proportions of volatile renewable energy, this added uncertainty from generation must also be faced. Conventional electricity market designs cope with uncertainty by running two markets: a day ahead or pre-dispatch market that is cleared ahe...

where L(t) is a given matrix. Unlike the deterministic setting, when the state is a random variable one cannot directly use the variational optimality conditions since the adjoint equation λ̇ = −∂xH cannot describe all possible random evolutions of x(t). We must resort to dynamic programming. We next consider dynamic programming for stochastic systems through the derivation of the stochastic Ham...