In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost of control is proportional to the magnitude of...

We give weak conditions for a continuous time optimal control problem with one-dimensional state space to have monotone optimal trajectories. These conditions include a concavity condition on the Lagrange function. If that condition is changed to strict concavity, then all optimal trajectories...

In this note we formulate an optimality problem for Stochastic process with a regime absorbing state. We present a solution for this problem as a pair of differential equations that are recusrsively linked. As an application I obtain an analytical for the Merton portfolio problem in a case for a...

Consider robust utility maximization with an irreversible consumption habit, where an agent concerned about model ambiguity is unwilling to decrease consumption and must simultaneously contend with a disutility (i.e., an adjustment cost) due to a consumption increase. While the optimization is a...

Ai and Li [2015] introduced a problem at the interface of the neoclassical investment and dynamic contract theories. Specifically, the authors consider the optimal design of a contract that provides sufficient incentives to the management for it to implement the shareholder’s investment plan...

Diversification plays an important role in financial theory and lays the foundation for financial risk management. However, its role is greatly weakened when systemic risk events occur. In this paper, we study portfolio selection against systemic risk from the perspective of individual...

In this paper, we consider a company that can satisfy customers' demands for a product using two alternative sourcing strategies: (1) purchasing new products from outside sources (such as an international partner) or (2) collecting cores (used products) and remanufacturing them. As the purchase...

The COVID-19 pandemic has ravaged almost every part of the world, causing severe loss of life and economic damage to the world economy. This study proposes a mathematical model of SARS-COV-2 by considering the high-risk population. We establish the local and global stability of the model based...

The burden of illicit drug use and terrorism has become a significant health and social problem in many developing countries. Illicit drug use and terrorism have negatively affected the economy and development of some nations because the death rate due to these two phenomena is increasing daily,...

Purpose The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game. Design/methodology/approach In contrast to the existing literature, the authors do not assume that after splitting, players will...

This study is concerned with applying fractional calculus in modelling tuberculosis (TB) transmission dynamics. A new six-dimensional fractional-order mathematical model in the sense of the Caputo derivative operator is formulated to capture memory effects in the spread process of tuberculosis....

Land subsidence threatens the living conditions of roughly 1.2 billion people worldwide in deltaic regions characterized by soft top soil. Economic activity in deltaic regions requires lowering the groundwater levels to keep the land sufficiently dry to maintain productivity, which, however,...