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Malliavin method for optimal investment in financial markets with memory

Qiguang An, Guoqing Zhao, Gaofeng Zong (2016)

Open Mathematics

We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market....

Minimal supersolutions of BSDEs with lower semicontinuous generators

Gregor Heyne, Michael Kupper, Christoph Mainberger (2014)

Annales de l'I.H.P. Probabilités et statistiques

We study minimal supersolutions of backward stochastic differential equations. We show the existence and uniqueness of the minimal supersolution, if the generator is jointly lower semicontinuous, bounded from below by an affine function of the control variable, and satisfies a specific normalization property. Semimartingale convergence is used to establish the main result.

Models for stochastic mortality

Jan Iwanik (2007)

Applicationes Mathematicae

This paper is an attempt to present and analyse stochastic mortality models. We propose a couple of continuous-time stochastic models that are natural generalizations of the Gompertz law in the sense that they reduce to the Gompertz function when the volatility parameter is zero. We provide a statistical analysis of the available demographic data to show that the models fit historical data well. Finally, we give some practical examples for the multidimensional models.

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