Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.

Coordinating Pricing and Inventory Control in a Fluctuating Environment

This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.

Optimal regulation of uncertain dynamic systems using adaptive dynamic programming

In this tutorial paper,the finite-horizon optimal adaptive regulation of linear and nonlinear dynamic systems with unknown system dynamics is presented in a forward-in-time manner using adaptive dynamic programming(ADP).An adaptive estimator(AE)is introduced with the idea of Q-learning to relax the requirement of system dynamics in the case of linear system,while neural network-based identifier is utilised for nonlinear systems.The time-varying nature of the solution to the Bellman/Hamilton–Jacobi–Bellman equation is handled by utilising a time-dependent basis function,while the terminal constraint is incorporated as part of the update law of the AE/Identifier in solving the optimal feedback control.Utilising an initial admissible control,the proposed optimal regulation scheme of the uncertain linear and nonlinear system yields a forward-in-time and online solution without using value and/or policy iterations.An adaptive observer is utilised for linear systems in order to relax the need for state availability so that the optimal adaptive control design depends only on the reconstructed states.Finally,the optimal control is covered for nonlinear-networked control systems where in the feedback loop is closed via a communication network.Effectiveness of the proposed approach is verified by simulation results.The end result is a variant of a roll-out scheme in ADP wherein an initial admissible policy is selected as the base policy and the control policy is enhanced using a one-time policy improvement at each sampling interval.