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A new stochastic control problem of population dynamics under partial observation is formulated and analyzed both mathematically and numerically, with an emphasis on environmental and ecological problems. The decision-maker can only…

We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic…

We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field…

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

We consider an optimal stochastic impulse control problem over an infinite time horizon motivated by a model of irreversible investment choices with fixed adjustment costs. By employing techniques of viscosity solutions and relying on…

Optimal allocation of agricultural water in the event of droughts is an important global problem. In addressing this problem, many aspects, including the welfare of farmers, the economy, and the environment, must be considered. Under this…

We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…

This paper studies a finite horizon utility maximization problem on excessive consumption under a drawdown constraint. Our control problem is an extension of the one considered in Bahman et al. (2019) to the model with a finite horizon and…

We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of…

Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in…

This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here,…

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a…

Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…

We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…

In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial…

In this paper we study an optimal portfolio selection problem under instantaneous price impact. Based on some empirical analysis in the literature, we model such impact as a concave function of the trading size when the trading size is…

The present paper addresses the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines. The optimal survival function is…

We introduce a method for approximating viscosity solutions of stationary degenerate elliptic Hamilton--Jacobi--Bellman equations on bounded domains arising in stochastic exit-time control. Viscosity enforcement is formulated as a min--max…