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Optimal and Near-Optimal (s,S) Inventory Policies for Levy Demand Processes

Robin O. Roundy, Gennady Samorodnitsky (2010)

RAIRO - Operations Research

A Levy jump process is a continuous-time, real-valued stochastic process which has independent and stationary increments, with no Brownian component. We study some of the fundamental properties of Levy jump processes and develop (s,S) inventory models for them. Of particular interest to us is the gamma-distributed Levy process, in which the demand that occurs in a fixed period of time has a gamma distribution. We study the relevant properties of these processes, and we develop a quadratically convergent...

Optimal closing of a pair trade with a model containing jumps

Stig Larsson, Carl Lindberg, Marcus Warfheimer (2013)

Applications of Mathematics

A pair trade is a portfolio consisting of a long position in one asset and a short position in another, and it is a widely used investment strategy in the financial industry. Recently, Ekström, Lindberg, and Tysk studied the problem of optimally closing a pair trading strategy when the difference of the two assets is modelled by an Ornstein-Uhlenbeck process. In the present work the model is generalized to also include jumps. More precisely, we assume that the difference between the assets is an...

Optimal stopping for Markov Processes

Massimo Lorenzani (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota presentiamo dei nuovi risultati sul problema di tempo d’arresto ottimale per processi di Markov con tempo discreto.

Optimal stopping of a risk process

Elżbieta Ferenstein, Andrzej Sierociński (1997)

Applicationes Mathematicae

Optimal stopping time problems for a risk process U t = u + c t - n = 0 N ( t ) X n where the number N(t) of losses up to time t is a general renewal process and the sequence of X i ’s represents successive losses are studied. N(t) and X i ’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

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