Related papers: Explicit Solutions for Optimal Resource Extraction…
Oil prices above $100/barrel values have proven unaffordable for the world economy, while lower prices have proven unaffordable for unconventional oil sources, resulting in a frantic price swing since 2007-2008. We identify and combine for…
We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function $f$ and our current net worth as $X(t)$ for any $t$, we invest an amount $f(X(t))$ in the market. We need a fortune of $M$…
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded $L^{1}$-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing…
This paper studies the problem of the deterministic version of the Verification Theorem for the optimal m-states switching in infinite horizon under Markovian framework with arbitrary switching cost functions. The problem is formulated as…
In this work, we consider the optimal portfolio selection problem under hard constraints on trading volume amounts when the dynamics of the risky asset returns are governed by a discrete-time approximation of the Markov-modulated geometric…
We study the stochastic dynamics of natural resources under the threat of ecological regime shifts. We establish a Pareto optimal framework of regime shift detection under uncertainty that minimizes the delay with which economic agents…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
We find a maximum principle for general non-Markovian semi-martingales. We do so by describing the adjoint processes with non-anticipating stochastic derivatives in a martingale random field setting. In the case of the L\'evy processes this…
Consider the discounted optimal stopping problem for a real valued Markov process with only positive jumps. We provide a theorem to verify that the optimal stopping region has the form {x >= x^*} for some critical threshold x^*, and a…
We study a dynamic portfolio optimization problem related to convergence trading, which is an investment strategy that exploits temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
At present, the problem to steer a non-Markovian process with minimum energy between specified end-point marginal distributions remains unsolved. Herein, we consider the special case for a non-Markovian process y(t) which, however, assumes…
Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which…
We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of…
In commodity markets the convergence of futures towards spot prices, at the expiration of the contract, is usually justified by no-arbitrage arguments. In this article, we propose an alternative approach that relies on the expected profit…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
In this paper we study a system of variational inequalities where the operator is non-local, possibly degenerate and of second order. A special case of this type of problem occurs in the context of optimal switching problems when the…
This paper investigates the problem of energy-optimal control for autonomous underwater vehicles (AUVs). To improve the endurance of AUVs, we propose a novel energy-optimal control scheme based on the economic model predictive control (MPC)…