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We study the optimal consumption, investment and lifeinsurance purchase and selection strategies for a wage-earner with an uncertain lifetime with access to a financial market comprised of one risk-free security and one risky-asset whose prices evolve according to linear diffusions modulated by a continuous-time stochastic process determined by an additional diffusive nonlinear stochastic differential equation. The process modulating the linear diffusions may be regarded as an indicator describing the state of the economy in a given instant of time. Additionally, we allow the Brownian motions driving each of these equations to be correlated. The lifeinsurance market under consideration herein consists of a fixed number of providers offering pairwise distinct contracts. We use dynamic programming techniques to characterize the solutions to the problem described above for a general family of utility functions, studying the case of discounted constant relative risk aversion utilities with more detail. [ABSTRACT FROM AUTHOR]

A controlled discrete-time stochastic process is proposed as a model for the state of a machine. In the proposed model, normal and random wear of the machine are considered. The random wear of the machine during a time unit can be either a discrete or a continuous random variable. The objective is to find a control policy that maximises the profits generated by the machine over its useful lifetime. In this problem, the optimiser must decide whether to do or not to do the maintenance work on the machine at each time unit. The significance of the paper is that the final time in the optimal control problem is a random variable denoting the first time the machine must be replaced. To obtain the optimal control, one can try to solve the dynamic programming equation, which reduces to a difference or an integral equation, satisfied by the value function. Finally, particular cases are solved exactly, or approximately, and explicitly to demonstrate and validate the proposed model. [ABSTRACT FROM AUTHOR]

We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that it involves two adjoint optimal stopping times adapted to a pair of filtrations, the traditional increasing one and another, decreasing. They are the keys of the time symmetry of the construction, which can be regarded as a generalization of 'Schrödinger's problem' (1931–1932) to space-time domains. The relation with the notion of 'Hidden diffusions' is also described. [ABSTRACT FROM AUTHOR]

The control of a stochastic manufacturing system that executes capital asset repairs and remanufacturing in an integrated system is examined. The remanufacturing resources respond to planned returns of worn-out equipment at the end of their expected life and unplanned returns triggered by major equipment failures. Remanufacturing operations for planned demand can be executed at different rates and costs corresponding to different replacement and repair modes. The replacement components inventory is provided by an upstream supply with random lead times. The objective is to determine a control policy for both the supply and remanufacturing activities that minimises the average repair/replacement, acquisition and inventory/shortage total cost over an infinite horizon. We propose a suboptimal joint remanufacturing and supply control policy, composed of a multi-hedging point policy (MHPP) for the remanufacturing stage and an (s, Q) policy for the replacement parts supply. The MHPP is based on two inventory thresholds that trigger the use of predefined remanufacturing modes. Control policy parameters are obtained combining analytical modelling, simulation experiments and response surface methodology. The effects of the distribution, mean and variability of the lead time are tested and a sensitivity analysis of cost parameters is conducted to validate the proposed control policy. We also show that our policy leads to a significant cost reduction as compared to a combination of a hedging point policy (HPP) and an (s, Q) policy. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence and uniqueness of solution for the optimal control problem governed by the stochastic FitzHugh–Nagumo equation driven by a Gaussian noise. First-order conditions of optimality are also obtained. [ABSTRACT FROM AUTHOR]