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Poisson's equation plays a fundamental role as a tool for performance evaluation and optimization of Markov chains. For continuous-time birth-death chains with possibly unbounded transition and cost rates as addressed herein, when…

We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines wether the optimal investment problem on a local martingale financial…

We consider an inventory system whose state is modeled by a L\'{e}vy process. There are two types of costs--the running costs and the inventory control costs. The running costs (also known as the holding/penalty costs) are incurred…

We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or…

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…

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…

We study the impact of learning on the optimal policy and the time-to-decision in an infinite-horizon Bayesian sequential decision model with two irreversible alternatives, exit and expansion. In our model, a firm undertakes a small-scale…

In this note, merging ideas from Loeffen (2009) and Renaud (2019), we prove that an (a,b)-strategy maximizes dividend payments subject to fixed transaction costs in a spectrally negative L\'evy model with Parisian ruin, as long as the tail…

In this paper we deal with the optimal bankruptcy problem for an agent who can optimally allocate her consumption rate, the amount of capital invested in the risky asset as well as her leisure time. In our framework, the agent is endowed by…

Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches…

The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities decay as exp(-lambda|x|) or…

We introduce a novel framework for computing optimal randomized security policies in networked domains which extends previous approaches in several ways. First, we extend previous linear programming techniques for Stackelberg security games…

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose…

Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…

This paper concerns an optimal impulse control problem associated with a refracted L\'{e}vy process, involving the reduction of reserves to a predetermined level whenever they exceed a specified threshold. The ruin time is determined by…

In this paper we provide a self-contained exposition of the problem of sustaining a constant consumption level in a Ramsey model. Our focus is on the case in which the output capital-ratio is random. After a brief review of the known…

We consider stochastic control systems affected by a fast mean reverting volatility $Y(t)$ driven by a pure jump L\'evy process. Motivated by a large literature on financial models, we assume that $Y(t)$ evolves at a faster time scale…

Prediction of events in financial markets is every investor's dream and, usually, wishful thinking. From a more general, economic and societal viewpoint, the identification of indicators for large events is highly desirable to assess…

Peters (2011a) defined an optimal leverage which maximizes the time-average growth rate of an investment held at constant leverage. It was hypothesized that this optimal leverage is attracted to 1, such that, e.g., leveraging an investment…

This paper studies the bailout optimal dividend problem with regime switching under the constraint that dividend payments can be made only at the arrival times of an independent Poisson process while capital can be injected continuously in…