Partially reversible capital investment with both fixed and proportional costs under demand risk (Financial Modeling and Analysis)

This study investigates a firm's capital expansion and reduction policy with both fixed and proportional costs when the output demand follows the geometric Brownian motion. We formulate the firm's problem as an impulse control problem and solve it by using quasi-variational inequalities. Through numerical analysis, we find that the output demand risk delays the capital expansion and reduction. Furthermore, the output demand risk decreases the magnitude of capital expansion, but it increases that of capital reduction

Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk

Environmental management and restoration should be designed such that the risk and uncertainty owing to nonlinear stochastic systems can be successfully addressed. We apply the robustified dynamic Orlicz risk to the modeling and analysis of environmental management and restoration to consider both the risk and uncertainty within a unified theory. We focus on the control of a jump-driven hybrid stochastic system that represents macrophyte dynamics. The dynamic programming equation based on the Orlicz risk is first obtained heuristically, from which the associated Hamilton-Jacobi-Bellman (HJB) equation is derived. In the proposed Orlicz risk, the risk aversion of the decision-maker is represented by a power coefficient that resembles a certainty equivalence, whereas the uncertainty aversion is represented by the Kullback-Leibler divergence, in which the risk and uncertainty are handled consistently and separately. The HJB equation includes a new state-dependent discount factor that arises from the uncertainty aversion, which leads to a unique, nonlinear, and nonlocal term. The link between the proposed and classical stochastic control problems is discussed with a focus on control-dependent discount rates. We propose a finite difference method for computing the HJB equation. Finally, the proposed model is applied to an optimal harvesting problem for macrophytes in a brackish lake that contains both growing and drifting populations

Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge

We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is a superposition of Ornstein-Uhlenbeck processes (supOU process), generating a sub-exponential autocorrelation function observed in actual data. The integral operator Riccati equation is heuristically derived to determine the optimal control of the infinite-dimensional system. In addition, its finite-dimensional version is derived with a discretized distribution of the reversion speed and computed by a finite difference scheme. The optimality of the Riccati equation is analyzed by a verification argument. The supOU process is parameterized based on the actual data of a perennial river. The convergence of the numerical scheme is analyzed through computational experiments. Finally, we demonstrate the application of the proposed model to realistic problems along with the Kolmogorov backward equation for the performance evaluation of controls