Related papers: Optimal Consumption in the Stochastic Ramsey Probl…
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit…
We study a problem of utility maximization under model uncertainty with information including jumps. We prove first that the value process of the robust stochastic control problem is described by the solution of a quadratic-exponential…
This paper provides a dual formulation of the optimal consumption problem with internal multiplicative habit formation. In this problem, the agent derives utility from the ratio of consumption to the internal habit component. Due to this…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety…
This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite…
This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the…
We revisit the classical Merton consumption--investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $\alpha$-integral, interpolating between It\^{o}, Stratonovich, and…
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
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…
This paper examines a continuous time intertemporal consumption and portfolio choice problem with a stochastic differential utility preference of Epstein-Zin type for a robust investor, who worries about model misspecification and seeks…
We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…
We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The…
This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed…
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…
The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given…