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Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games

César U. S. Solis, Julio B. Clempner, Alexander S. Poznyak (2019)

Kybernetika

This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves defenders and...

Hedging in complete markets driven by normal martingales

Youssef El-Khatib, Nicolas Privault (2003)

Applicationes Mathematicae

This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket M , M t , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.

How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) 𝒰 a d 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) [ 0 , 1 ] t . (2). The results are nonlocal and new.

Incompleteness of the bond market with Lévy noise under the physical measure

Michał Barski (2015)

Banach Center Publications

The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.

Indices económicos. Modelo dinámico de inversión.

M.ª Angeles Fernández Fernández (1986)

Trabajos de Investigación Operativa

Se estudia el problema de inversión en un mercado en donde las rentabilidades aleatorias de los títulos satisfacen una relación temporal con rentabilidades anteriores y las interrelaciones vendrán dadas a través de unos índices, uno común a todos los títulos y otro específico del sector en que pueda incluirse cada título.

Indifference valuation in incomplete binomial models

M. Musiela, E. Sokolova, T. Zariphopoulou (2010)

MathematicS In Action

The indifference valuation problem in incomplete binomial models is analyzed. The model is more general than the ones studied so far, because the stochastic factor, which generates the market incompleteness, may affect the transition propabilities and/or the values of the traded asset as well as the claim’s payoff. Two pricing algorithms are constructed which use, respectively, the minimal martingale and the minimal entropy measures. We study in detail the interplay among the different kinds of...

Currently displaying 421 – 440 of 982