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We study a problem of optimal investment/consumption over an infinite horizon in a market consisting of a liquid and an illiquid asset. The liquid asset is observed and can be traded continuously, while the illiquid one can only be traded…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
This paper studies the optimal control problems of stochastic evolution equations with infinite delay of general functional type. By introducing a non-anticipative path derivative and its infinite-window dual operator, we derive the…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
In this paper we study a utility maximization problem with both optimal control and optimal stopping in a finite time horizon. The value function can be characterized by a variational equation that involves a free boundary problem of a…
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
This article explores an optimal stopping problem for branching diffusion processes. It consists in looking for optimal stopping lines, a type of stopping time that maintains the branching structure of the processes under analysis. By using…
Specifying reward functions for complex tasks like object manipulation or driving is challenging to do by hand. Reward learning seeks to address this by learning a reward model using human feedback on selected query policies. This shifts…
We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed…
This paper consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modeled as additional food provided prey-predator system with Holling Type-III functional…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
We propose a formulation for approximate constrained nonlinear output-feedback stochastic model predictive control. Starting from the ideal but intractable stochastic optimal control problem (OCP), which involves the optimization over…
In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…